Research ArticleOpinion Dynamics Model Based on Cognitive StylesField-Dependence and Field-Independence

Xi Chen12 Shen Zhao12 and Wei Li 12

1School of Artificial Intelligence and Automation Huazhong University of Science and Technology Wuhan 430074 China2Image Processing and Intelligent Control Key Laboratory of the Education Ministry of China Wuhan 430074 China

Correspondence should be addressed to Wei Li liwei0828mailhusteducn

Received 18 September 2018 Revised 5 January 2019 Accepted 26 January 2019 Published 11 February 2019

Academic Editor Sara Dadras

Copyright copy 2019 Xi Chen et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Two distinct cognitive styles exist from the perspective of cognition field-dependence and field-independence In most publicopinion dynamics models people only consider that individuals update their opinions through interactionswith other individualsThis represents the field-dependent cognitive style of the individual The field-independent cognitive style is ignored in such casesWe consider both cognitive styles in public opinion dynamics and propose a public opinion evolution model based on cognitivestyles (CS model) The opinions of neighbors and experiences of the individual represent field-dependent cognition and field-independent cognition respectively and the individual combines both cognitive styles to update hisher own opinion In theproposed model the experience parameter is designed to represent the weight of the current opinion in terms of the individualrsquosexperiences and the cognitive parameter is proposed to represent the tendencies of hisher cognitive styles We experimentallyverify that the CS and HegselmannndashKrause (HK) models are similar in terms of public opinion evolution trends with an increasein radius of confidence the steady state of a social system shifts from divergence to polarization and eventually reaches consensusConsidering that individuals from different cultures have different degrees of inclination for the two styles we present experimentsfocusing on cognitive parameter and experience parameter and analyze the evolutionary trends of opinion dynamics in differentstyles We find that when an individual has a greater tendency toward the field-independent cognitive style under the influenceof culture the time required for a social system to reach a steady state will increase the system will have greater difficultly inreaching consensus mirroring the evolutionary trends in public opinion in the context of eastern and western cultures The CSmodel constitutes an opinion dynamics model that is more consistent with the real world and may also serve as a basis for futurecross-cultural research

1 Introduction

Research on public opinion dynamics has always involvedmany fields of research including sociology psychologyinformatics and physics These studies are mainly focusedon the evolution formation and consensus of grouppublicopinions Public opinion can have a substantial impact onpublic policy The more salient the issues the stronger theimpact [1] Social policy and public opinion are utilizedas a feedback system [2] The public health communityof America models public health problems by extendingopinion dynamics and analyzes the correlation betweendiseases and behaviors such as alcohol and tobacco use tostudy corresponding public policy interventions [3] Chen[4] believes that different individuals have attributes that

can affect opinion evolution He presented a public opinioncontrol strategy based on public authority and makes use ofa public opinion dynamics model (the HegselmannndashKrause(HK) model [5]) to verify the effectiveness of policies Bothwestern and eastern scholars have studied public opiniondynamics One of the most important goals of this researchis to detect public opinion to understand the evolution ofpublic opinion as it relates to public affairs which providesinsight into real human attitude-formation mechanismsThisexercise can aid governments in making optimal decisions

Public opinion is a typical complex system Influenced bysocial and economic factors the evolution of public opinionpresents complexity openness and nonlinearity [6] Theevolution of public opinion in complex systems is one of thecore issues in nonlinear science [7 8] The model of opinion

HindawiComplexityVolume 2019 Article ID 2864124 12 pageshttpsdoiorg10115520192864124

2 Complexity

dynamics mainly explains the nonlinear characteristics ofthe evolution of public opinion the goal being to studythe evolution process of public opinion [9ndash11] The opiniondynamics can be traced back to 1956 when French proposeda simple discrete mathematical model to study the behavioralcomplexity of a team [12] Thereafter many scholars haveproposed many public opinion dynamic models based onvarious rules In the Voter model individuals are affected byneighbors and change their opinions to mirror those of theirneighbors [13] The majority rule model has been proposed[14] based on the ldquoconformity behaviorrdquo of social psychology[15] The difference between this model and the Voter modelis that the individual changes hisher opinion tomatch that ofthe majority of hisher neighbors Some researchers are of theopinion that the higher the number of neighbors the greaterthe chance that an individualrsquos opinion will be influencedby hisher neighbors In other words a higher number ofneighbors can be more persuasive The Sznajd model is theimproved Voter model [16] The basic idea is that if two ormore neighbors were to persuade an individual and thenheshe would be more inclined to align hisher opinion totheirs

Almost all of the above models and their extendedmodels express individual opinions with discrete values andusually use -1 (against) 0 (neutral) and +1 (concurring) toexpress opinions respectively In real life there are oftenfuzzy value phenomena that are difficult to be accuratelydivided by individual opinions Therefore some scholarsuse the numerical values within the interval [0 1] to rep-resent individual opinions which is called a continuousopinion dynamics model The continuous opinion dynamicsmodel mainly includes the Deffuant model [17] and the HKmodel [5] These two models are also known as boundedconfidence models because they both follow the rule ofbounded confidence that is individuals only change theiropinions due to their neighbors within the radius of con-fidence [18] which conforms to the ldquoselective exposurerdquo ofsocial psychology [19] Recently the bounded confidencemodel has received a significant response in the field ofpublic opinion dynamics Many scholars have made differentimprovements on it and suggested extensions to it in orderto reasonably study the evolution of public opinion Pinedaet al [20] studied the Deffuant model with noisy effectsChen et al [21] considered three types of different socialacquaintance networks (independence-priority acquaintancenetwork kinship-priority acquaintance network and hybridacquaintance network) and utilized the Deffuant model toconduct experimental simulation analysis of public opinionevolution These three acquaintance networks are similarto networks of western acquaintances traditional Chineseacquaintances and modern Chinese acquaintances respec-tively Finally a culture-policy-drivenmechanism for opiniondynamics was proposed based on the simulation resultsGrauwinrsquos research on the Deffuant model found that whenthe difference in individual opinions is greater than theconfidence radius opinions correction with a certain prob-ability was beneficial to the convergence and uniformityof opinions [22] If Deffuant model concerns the slowinteraction between two individuals the HK model refers

to the interactions between multiple individuals SimilarlyMiguel [23] notes the effects of noise on the classical HKmodel and showed that at a certain probability individualshave the opportunity to change their opinions spontaneouslyLorenz [24] believes that there is heterogeneity in the con-fidence radius of individuals According to the differencesin the confidence radius individuals can be divided intoopen-minded individuals and closed-minded individuals Su[25] believes that the HK model should be considered fordirected networks In the Bulletin Board System (BBS) anindividual can be influenced by opinion providers but cannotinfluence the opinions of opinion providers This is a typicalobservation and learning process and its conclusions areof great significance to the formation and decision-makingprocess of group opinions Some scholars have introducedldquoparanoidrdquo psychology into the HK model to study theinfluence of a few paranoid individuals in the social groupon the evolution of opinions [26] Regarding the classicalHK model Fu proposes an evolution model of opinion thatconsiders the parameters of self-confidence [27] Confidenceis reflected in the degree of persistence in self-confidenceand nonconfidence is reflected in the degree of trust inother peoplersquos opinions Some scholars have studied the HKopinion evolution model with competitive opinion leaders[28] Some scholars believe that the individualrsquos confidenceradius should not be fixed and should be influenced byindividual confidence and neighbor influence Thus a time-varying bounded confidencemodel is proposed [29] It can beseen from the above that many scholars have improved andexpanded the classical public opinion dynamics to make itmore consistent with reality so as to explore the internal lawsandmechanisms of real social public opinion However fromthe cognitive perspective in both theDeffuantmodel andHKmodel individuals only cognize through interactions withtheir surrounding neighbors before updating their opinions

As per the Oxford dictionary cognition is ldquothe mentalaction or process of acquiring knowledge and understandingthrough thought experience and the sensesrdquo [30] In the evo-lution of public opinion the interaction between individualsis a cognitive process Individuals process information viacognition to update their ownopinionsWitkin [31] suggestedthat there are two cognitive styles for processing informationthe field-dependent and field-independent cognitive stylesWitkin also designed the embedded figures test (EFT) in1974 which is a famousmeasure to distinguish between field-independence and field-dependence He calls those who relytoo much on their environment to make judgments as fielddependents and those who judge by themselves as field-independent [32] The field-dependent cognitive style refersto the tendency of people to rely on external references orexternal environmental cues when processing informationThe field-independent cognitive style refers to the tendencyof people to process information based on internal perceptualcues When the two cognitive styles of field-dependence andfield-independence were proposed they quickly became aresearch hotspot in the field of cognitive psychology [33ndash36] Since then the cognition method has been widelystudied in the educational field [37ndash40] However researchon social psychology has revealed that field-dependence and

Complexity 3

field-independence may be cultural variations of cognitivestyle People from different cultural backgrounds have dif-ferent tendencies toward these two cognitive styles [41] Onestudy has suggested that Chinese people tend toward field-dependence more than American people which may be theresult of cultural preferences [42]

Currently most research on opinion dynamics focuseson the idea that an entire social system evolves based oninteractions between individuals For example in the HKmodel an individual updates hisher opinions by averagingthe opinions of all neighbors that meet a given confidencethreshold [43] Because this model relies on the opinions ofothers (ie on external references) it is based on the cog-nitive style of individual field-dependence Although thereare many improved HK models that have introduced theconcepts of self-reliance bigotry and individuals consideringtheir own opinions during the evolution process [26 27 44]these are merely copies of the original or current opinions ofindividuals and are not truly based on internal cues Basedon the above information it can be seen that in classicalopinion evolutionmodels and their extensions the individualfield-dependent cognitive style has been considered butthe individual field-independent cognitive style has beenignored However people in the real world are complex andoften utilize both cognitive stylesTherefore it is necessary toconsider the individual field-independent cognitive style inopinion dynamics

In this paper we introduce the field-independent cogni-tive style of individuals into opinion dynamics and propose apublic opinion evolution model based on cognitive styles (theCS model) which has the following two main motivations

(i) Psychology is implicitly responsible for individualexternal behavior Referring to psychology researchers con-stantly formulate relevant rules to promote the developmentand improvement of the opinion dynamics model Howeverin reality the change in individual opinions is the resultof individual cognition Thus it is necessary to introducecognitive psychology more deeply into the opinion dynamicsmodel

(ii) The classical bounded confidence model (taking theHK model as an example) only considers the interactionof individuals with their neighbors within the radius ofconfidence In a sense this can be regarded as part of theindividualrsquos field-dependent cognitive style However in thereal evolution of opinions when an individualrsquos opinions areupdated they are not only influenced by their neighborsbut also influenced by hisher own experience or thinkingFor example in the scenario of public opinion evolutionon a policy each individualrsquos opinion is not only influencedby other individuals but also based on hisher thoughts orexperience

The contribution of our proposed method is to intro-duce the individualrsquos field-independent cognitive style basedon the classical HK model The experience parameter isused to construct the field-independent cognitive part ofthe individual and the classical HK model is regarded asthe field-dependent cognitive part of the individual It isproposed that cognitive parameter not only represents the

tendency of individuals to the field-independent or field-dependent cognitive style but also integrates the individualrsquosfield independent and field-dependent cognitive styles whenheshe updates hisher opinions Our improvement allowsindividuals to update their opinions not only according totheir neighborsrsquo opinions within the bounded confidence(HKmodel field-dependent cognition) but also according totheir own experiences (field-independent cognition) In thisway the HK model is enriched to make it more realistic

The rest of this paper is arranged as follows In Section 2we provide a detailed discussion of the two cognitive stylesof individual field-independence and field-dependence andpropose a public opinion dynamics model considering dif-ferent cognitive styles Section 3 presents the numerical sim-ulation results and analysis of the CS model The discussionand conclusions are presented in Section 4

2 Model

21 Field-Independent and Field-Dependent Cognitive Stylesof Individuals From the description of cognitive psychologyfield-independence and field-dependence are two cognitivestyles that emphasize the concept that individuals differ inprocessing information [45] The former focuses on internalperception and the latter focuses on external influences incognitive processes [46] In most public opinion dynam-ics models the interactions between individuals and theirneighbors (external) are the main mechanism for updatingindividual opinions These models only consider the cog-nitive style of individual field-dependence However in thereal world field-independent cognitive styles of individualsalso exist during the evolution of public opinion In thefields of psychology or pedagogy these types of cognitivestudies tend to adopt absolute definitions which representdichotomous thinking In other words a person eitherhas a field-independent cognitive style or field-dependentcognitive style [47ndash49] In a public opinion evolution systemif individuals are absolutely field-independent the systemwill develop various opinions and have difficulty reachingpolarization let alone convergence This concept does notagree with real human sociality [50] or major phenomenain reality such as mass incidents [51 52] To be accurateindividuals in a social system are more complex and shouldhave both field-independent and field-dependent cognitivestyles simultaneously In other words in the process ofpublic opinion evolution an individual will be influencedby external factors but will be also guided by internal cuesHowever because of the influence of culture and otherfactors certain individuals tend to be more field-dependentcognitive and others are more inclined to field-independentDuring the evolution of public opinion the opinions ofindividuals after interactions with others should be code-termined by the two cognitive styles Based on research onthe feeding behavior of birds the operational mechanismof the particle swarm method simulates biological groupsand their social behavior Each iteration changes individualvelocities according to individual experiences and the grouprsquosflight experiences to make corresponding adjustments [53]

4 Complexity

This is consistent with the concept that individuals updatetheir opinions according to both field-dependence and field-independence in the evolution of public opinion In the fieldof statistical physics as per the model proposed by relevantresearch agents (atoms) change their state based on noiseor temperature (internal characteristics) as well as externalfactors (interaction with neighbors) [54 55] In the processof public opinion evolution the traditional opinion dynamicsmodel (the HK model) only considers the cognitive styleof individual field-dependence it is necessary to introducethe cognitive style of individual field-independence In thismanner the model can bemademore consistent with the realworld

22 CS Model We consider the classical HK model as anexample and consider the field-independent cognitive styleof individuals in this model To construct the HK model weconsider 119899 agents in a system the set of which is denotedas 119873 = 1 2 3 4 119899 where agent 119894 isin 119873 The opinionof agent 119894 at time 119905 is represented by 119909119894(119905) isin (0 1) Initiallyeach agent has an opinion 119909119894(0) where 119909119894(0) isin (0 1)The initial opinions of the agents in the system are subjectto a particular distribution such as a uniform or normaldistribution Each agent has its own threshold of confidence120576119894 When the difference between its opinion and the opinionsof its neighbors is less than the confidence threshold theagent will choose to interact with its neighbors The discrete-time HK model is described by

119909119894 (119905 + 1) =

11003816100381610038161003816119873119894 (119905)

1003816100381610038161003816sum119895isin119873119894(119905)

119909119895 (119905) 119873119894 (119905) = 0

119909119894 (119905) 119900119905ℎ119890119903119908119894119904119890(1)

where 119873119894(119905) = 119895 isin 119881 | |119909119894(119905) minus 119909119895(119905)| le 120576119894 is the opinionneighbor set of agent 119894 at time 119905 and |119873119894(119905)| is the number ofneighbor interactions

When the field-independent cognitive style of individualsis considered in public opinion dynamics we simplify thedefinition of cognition and form a corresponding hypothesisSuppose that during the evolution of public opinion in termsof the field-independent cognitive style the individual willgain opinions only through hisher own experiences Theexperiences of the individual are simplified as opinions inhisher memory and we only consider their opinions at thelast moment in discrete time Therefore we propose a publicopinion evolution model based on cognitive styles (the CSmodel) as described by

119909119894 (119905 + 1) = 119888 sdot [120596 sdot 119909119894 (119905) + (1 minus 120596) sdot 119909119894 (119905 minus 1)] + (1 minus 119888)

sdot 11003816100381610038161003816119873119894

1003816100381610038161003816sum119895isin119873119894

119909119895 (119905)

119873119894 (119905) = 119895 isin 119881 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 le 120576119894

(2)

120596 sdot 119909119894(119905) + (1 minus 120596) sdot 119909119894(119905 minus 1) is the opinion that agent119894gainsbased on the field-independent cognitive style 120596 is a setof experience parameters that represent the weight of theopinion at time 119905 on the agentrsquos experience (1 minus120596) represents

the weight of the opinion at time 119905 minus 1 on the agentrsquosexperience which is the opinion at the last moment inmemory (1|119873119894|) sum119895isin119873119894 119909119895(119905) is the opinion that agent 119894 gainsbased on the field-dependent cognitive style which is definedby the HK model 119888 is the set of cognitive parameters thatrepresents the tendency of an individualrsquos cognitive styleThe value of the cognitive parameter 119888 is the proportionof individual opinion determined by the field-independentcognitive style Therefore 1 - c represents the proportionof individual opinion determined by the field-dependentcognitive style 119888 + 1 minus 119888 = 1 which indicates that individualopinions are codetermined by the two cognitive styles Forexample in the process of marketing our opinions towards aproduct will be influenced by the opinions of our friends andrelatives and wewill also judge the product based on our ownexperience and finally determine our opinions The processof our opinions on the film is similar We are influenced byfilm reviews and we also make judgments based on our field-independent cognition Similarly in the CS model proposedin this paper for each iteration the individual opinion value isupdated according to the individualrsquos own experience (field-independent cognition) and the opinions values of otherneighboring individuals (field-dependent cognition)

3 Numerical Simulations

TheCSmodel was studied by utilizing agent-based modelingand simulations For the sake of convenience we assume thatthe social system is homogeneous meaning that all individ-uals in a given system have the same confidence thresholdand same tendency for cognitive styles Our simulations com-prised 1000 agents in the public opinion evolution systemThe relational network for the agents in the simulation systemwas fully connected which means that any agent could knowthe opinions of all other agents during the evolution ofpublic opinion The reason for selecting a fully connectednetwork was to avoid the effects of network topology onsimulation results The opinions of the agents are quantizedas continuous values between 0 and 1 To avoid the effects ofinitial opinions on the simulation results the initial opinionsof the agents followed a uniform distribution between 0 and1 In the experiments described below we mainly studiedthe influences of the individual field-independent and field-dependent cognitive styles (cognitive parameter 119888) and theinfluence of the individual experience parameter (120596) on theevolution of public opinion in the social system We definethe steady state of the system as follows if the opinion of allindividuals does not continue to change the system becomessteady [56] In addition when the difference between twoopinion values is less than 00001 we regard the two opinionsas the same opinion Two observation indicators were utilizedto measure the impact of these factors on the evolution ofpublic opinion The first is the steady state of the socialsystem which can be represented by the number of opinionclusters when the system reaches a steady state The other issteady time which is how long the system takes to reach asteady state The block diagram of the simulation experimentdesign is shown in Figure 1

Complexity 5

Opinion evolution system

field-independent cognition+

field-dependent cognition

Update opinion value

Start

End

Observation indicatorsof the system

Steady timeSteady state

Experiment AVerify the impact of cognitive

parameter

Experiment BVerify the impact of experience

parameter

Individual initial opinion value

YesNo

Is steady

Figure 1 Block diagram of the simulation experiment design

31 Impact of Field-Independence and Field-Dependence Cog-nitive Styles on Evolution of Public Opinion First we studythe impact of cognitive parameters (119888) on the evolution ofpublic opinion which represents the tendencies of individualcognitive styles In our simulations we consider a constantset of experience parameters (120596 = 05) to facilitate theanalysis of cognitive styles and their influence on publicopinion evolution Figure 2 presents the simulation resultsof the HK model with different confidence thresholds inwhich the X-axis represents the system evolution time andthe Y-axis represents the opinion values of individuals inthe system As shown in Figure 2 for the classical HKmodel with a confidence threshold of 01 there were fourclusters of opinion when the system reached a steady stateWhen the confidence threshold increased to 02 the entiresystem became polarized into two opinion clusters whenit reached a steady state With a confidence threshold of025 all opinions in the social system reached consensus ata steady state Therefore in the HK model the confidencethresholds of 01 02 and 025 correspond to divergencepolarization and consensus respectively which are the threesteady states of the social system In order to study the impactof cognitive styles on public opinion evolution for differentsteady states of a social system we set the confidence thresh-old to values of 120576119894 isin [01 02 021 022 023 024 025]Simultaneously we set the cognitive parameter to values of119888 isin [0 01 02 03 04 05 06 07 08 09]

Figure 3 presents the simulation results for the steadystate of the social systemwith different confidence thresholdsand cognitive parameters (119888) The green yellow and redrectangles represent divergence polarization and consensusrespectively which are the three steady states of the socialsystem When 119888 = 0 the model is equal to the classicalHK model If the confidence threshold is 01 regardlessof the cognitive parameter value the steady state of the

social system is divergence When the confidence thresholdis gradually changed from 02 to 025 the steady state ofthe social system gradually changes from polarization toconsensus One can see that when considering the field-independent cognitive style of individuals the tendency ofthe new model for the steady state of the system to changewith the confidence threshold is similar to that of the classicalHK model As the confidence threshold increases the steadystate of the system changes from divergence to polarizationand eventually reaches consensus However there are differ-ences between the new model and the classical HK modelWhen the confidence threshold is 021 the steady state ofthe system in the classical HK model is consensus but thesteady state of the system considering the field-independentcognitive style is still polarization When the confidencethreshold is 022 the steady state of the system in which thecognitive parameter value was nomore than 05 (119888 le 05) alsochanges to consensus but the steady state of the systemwherethe cognitive parameter value is no less than 06 (119888 ge 06) isstill polarization After the confidence threshold increases to023 except for the steady state of the system in which thecognitive parameter value was no less than 08 (119888 ge 08) thesteady state of the systems has already reached consensusOnce the confidence threshold reaches 024 regardless ofthe cognitive parameter value all steady states of the socialsystems reach consensus Based on the above analysis wecan conclude the value of the cognitive parameter has animpact on the steady state of a social system These resultsalso reveal that the tendencies of individuals toward field-independent and field-dependent cognitive styles have animpact on the evolution of public opinion The larger thevalue of the cognitive parameter (119888) the larger the proportionof individual opinions that are determined by the field-independent cognitive style Specifically individuals aremoreinclined toward the field-independent cognitive style during

6 Complexity

Confidence Threshold01

Confidence Threshold02

Confidence Threshold025

0

01

02

03

04

05

06

07

08

09

1O

pini

on

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

Figure 2 Opinion evolution results for the HK model with different confidence thresholds

0 01 02 03 04 05 06 07 08 09Cognitive parameters c

0102

021022023024025

Con

fiden

ce th

resh

old

Figure 3 Steady state of a social system with different confidencethresholds and cognitive parameters (119888)

the evolution of public opinion whichmakes it more difficultfor the steady state of the social system to reach consensusOnthe contrary the smaller the value of the cognitive parameter119888 the easier it is to reach consensus

To study the influence of cognitive styles on the steadytime of opinion evolution we compare the steady times withdifferent cognitive parameter values for the three steady statesof a social system (divergence polarization and consensus)Asmentioned previously the confidence thresholds we selectare 01 02 and 025 (120576119894 isin [01 02 025]) regardless of thecognitive parameter values the steady state of the social sys-tem always moves toward divergence polarization and con-vergence respectively In the same manner we set the cogni-tive parameter 119888 isin [0 01 02 03 04 05 06 07 08 09] inorder to study the impact of cognitive style on the steady timeof opinion evolution

Figure 4 presents the simulation results for the steadytime of the social system for different values of the cognitiveparameter (119888) for three steady states (divergence polarization

and consensus) When 119888 = 0 the model is equal to theclassical HKmodel One can see fromFigure 4 that comparedto the classical HK model (119888 = 0) the proposed systemrequires a longer time to reach steady state (119888 = 0) It can alsobe seen that irrespective of the steady state of the social system(divergence polarization or convergence) as the value of thecognitive parameter (119888) increases the time required for thesocial system to reach steady state increases This suggeststhat the more the individuals are inclined toward the field-independent cognitive style during the evolution of publicopinion the more time the social system requires to reach asteady state thus stability is more difficult to achieve

Above all we focus on analyzing the impact of thecognitive parameter (119888) on the evolution of public opinionWhen the cognitive parameter is 0 (119888 = 0) only theindividualrsquos field-dependent cognitive style is considered butthe individual field-independent cognitive style is ignoredAt this time the CS model degenerates into the classicalHK model When 119888 = 0 the simulation experimental datareflect the results of the evolution of the classical HK modelCompared with the classical HK model the CS model hasa longer evolution time and it is more difficult to reachconsensus in the system In addition the larger the valueof the cognitive parameter (119888) the greater the proportionof field-independent cognitive styles for individuals Thismeans that individuals have a stronger tendency to followthe field-independent cognitive style during the evolutionof public opinion Thus individuals will focus more oninternal perception and less on external influences whenupdating their own opinions In other words individualsare more likely to perform independent cognition and lesslikely to consider the opinions of their neighbors within theconfidence range However opinion dynamics is a fusion

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

Complexity 3

field-independence may be cultural variations of cognitivestyle People from different cultural backgrounds have dif-ferent tendencies toward these two cognitive styles [41] Onestudy has suggested that Chinese people tend toward field-dependence more than American people which may be theresult of cultural preferences [42]

Currently most research on opinion dynamics focuseson the idea that an entire social system evolves based oninteractions between individuals For example in the HKmodel an individual updates hisher opinions by averagingthe opinions of all neighbors that meet a given confidencethreshold [43] Because this model relies on the opinions ofothers (ie on external references) it is based on the cog-nitive style of individual field-dependence Although thereare many improved HK models that have introduced theconcepts of self-reliance bigotry and individuals consideringtheir own opinions during the evolution process [26 27 44]these are merely copies of the original or current opinions ofindividuals and are not truly based on internal cues Basedon the above information it can be seen that in classicalopinion evolutionmodels and their extensions the individualfield-dependent cognitive style has been considered butthe individual field-independent cognitive style has beenignored However people in the real world are complex andoften utilize both cognitive stylesTherefore it is necessary toconsider the individual field-independent cognitive style inopinion dynamics

In this paper we introduce the field-independent cogni-tive style of individuals into opinion dynamics and propose apublic opinion evolution model based on cognitive styles (theCS model) which has the following two main motivations

(i) Psychology is implicitly responsible for individualexternal behavior Referring to psychology researchers con-stantly formulate relevant rules to promote the developmentand improvement of the opinion dynamics model Howeverin reality the change in individual opinions is the resultof individual cognition Thus it is necessary to introducecognitive psychology more deeply into the opinion dynamicsmodel

(ii) The classical bounded confidence model (taking theHK model as an example) only considers the interactionof individuals with their neighbors within the radius ofconfidence In a sense this can be regarded as part of theindividualrsquos field-dependent cognitive style However in thereal evolution of opinions when an individualrsquos opinions areupdated they are not only influenced by their neighborsbut also influenced by hisher own experience or thinkingFor example in the scenario of public opinion evolutionon a policy each individualrsquos opinion is not only influencedby other individuals but also based on hisher thoughts orexperience

The contribution of our proposed method is to intro-duce the individualrsquos field-independent cognitive style basedon the classical HK model The experience parameter isused to construct the field-independent cognitive part ofthe individual and the classical HK model is regarded asthe field-dependent cognitive part of the individual It isproposed that cognitive parameter not only represents the

tendency of individuals to the field-independent or field-dependent cognitive style but also integrates the individualrsquosfield independent and field-dependent cognitive styles whenheshe updates hisher opinions Our improvement allowsindividuals to update their opinions not only according totheir neighborsrsquo opinions within the bounded confidence(HKmodel field-dependent cognition) but also according totheir own experiences (field-independent cognition) In thisway the HK model is enriched to make it more realistic

The rest of this paper is arranged as follows In Section 2we provide a detailed discussion of the two cognitive stylesof individual field-independence and field-dependence andpropose a public opinion dynamics model considering dif-ferent cognitive styles Section 3 presents the numerical sim-ulation results and analysis of the CS model The discussionand conclusions are presented in Section 4

2 Model

21 Field-Independent and Field-Dependent Cognitive Stylesof Individuals From the description of cognitive psychologyfield-independence and field-dependence are two cognitivestyles that emphasize the concept that individuals differ inprocessing information [45] The former focuses on internalperception and the latter focuses on external influences incognitive processes [46] In most public opinion dynam-ics models the interactions between individuals and theirneighbors (external) are the main mechanism for updatingindividual opinions These models only consider the cog-nitive style of individual field-dependence However in thereal world field-independent cognitive styles of individualsalso exist during the evolution of public opinion In thefields of psychology or pedagogy these types of cognitivestudies tend to adopt absolute definitions which representdichotomous thinking In other words a person eitherhas a field-independent cognitive style or field-dependentcognitive style [47ndash49] In a public opinion evolution systemif individuals are absolutely field-independent the systemwill develop various opinions and have difficulty reachingpolarization let alone convergence This concept does notagree with real human sociality [50] or major phenomenain reality such as mass incidents [51 52] To be accurateindividuals in a social system are more complex and shouldhave both field-independent and field-dependent cognitivestyles simultaneously In other words in the process ofpublic opinion evolution an individual will be influencedby external factors but will be also guided by internal cuesHowever because of the influence of culture and otherfactors certain individuals tend to be more field-dependentcognitive and others are more inclined to field-independentDuring the evolution of public opinion the opinions ofindividuals after interactions with others should be code-termined by the two cognitive styles Based on research onthe feeding behavior of birds the operational mechanismof the particle swarm method simulates biological groupsand their social behavior Each iteration changes individualvelocities according to individual experiences and the grouprsquosflight experiences to make corresponding adjustments [53]

4 Complexity

This is consistent with the concept that individuals updatetheir opinions according to both field-dependence and field-independence in the evolution of public opinion In the fieldof statistical physics as per the model proposed by relevantresearch agents (atoms) change their state based on noiseor temperature (internal characteristics) as well as externalfactors (interaction with neighbors) [54 55] In the processof public opinion evolution the traditional opinion dynamicsmodel (the HK model) only considers the cognitive styleof individual field-dependence it is necessary to introducethe cognitive style of individual field-independence In thismanner the model can bemademore consistent with the realworld

22 CS Model We consider the classical HK model as anexample and consider the field-independent cognitive styleof individuals in this model To construct the HK model weconsider 119899 agents in a system the set of which is denotedas 119873 = 1 2 3 4 119899 where agent 119894 isin 119873 The opinionof agent 119894 at time 119905 is represented by 119909119894(119905) isin (0 1) Initiallyeach agent has an opinion 119909119894(0) where 119909119894(0) isin (0 1)The initial opinions of the agents in the system are subjectto a particular distribution such as a uniform or normaldistribution Each agent has its own threshold of confidence120576119894 When the difference between its opinion and the opinionsof its neighbors is less than the confidence threshold theagent will choose to interact with its neighbors The discrete-time HK model is described by

119909119894 (119905 + 1) =

11003816100381610038161003816119873119894 (119905)

1003816100381610038161003816sum119895isin119873119894(119905)

119909119895 (119905) 119873119894 (119905) = 0

119909119894 (119905) 119900119905ℎ119890119903119908119894119904119890(1)

where 119873119894(119905) = 119895 isin 119881 | |119909119894(119905) minus 119909119895(119905)| le 120576119894 is the opinionneighbor set of agent 119894 at time 119905 and |119873119894(119905)| is the number ofneighbor interactions

When the field-independent cognitive style of individualsis considered in public opinion dynamics we simplify thedefinition of cognition and form a corresponding hypothesisSuppose that during the evolution of public opinion in termsof the field-independent cognitive style the individual willgain opinions only through hisher own experiences Theexperiences of the individual are simplified as opinions inhisher memory and we only consider their opinions at thelast moment in discrete time Therefore we propose a publicopinion evolution model based on cognitive styles (the CSmodel) as described by

119909119894 (119905 + 1) = 119888 sdot [120596 sdot 119909119894 (119905) + (1 minus 120596) sdot 119909119894 (119905 minus 1)] + (1 minus 119888)

sdot 11003816100381610038161003816119873119894

1003816100381610038161003816sum119895isin119873119894

119909119895 (119905)

119873119894 (119905) = 119895 isin 119881 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 le 120576119894

(2)

120596 sdot 119909119894(119905) + (1 minus 120596) sdot 119909119894(119905 minus 1) is the opinion that agent119894gainsbased on the field-independent cognitive style 120596 is a setof experience parameters that represent the weight of theopinion at time 119905 on the agentrsquos experience (1 minus120596) represents

the weight of the opinion at time 119905 minus 1 on the agentrsquosexperience which is the opinion at the last moment inmemory (1|119873119894|) sum119895isin119873119894 119909119895(119905) is the opinion that agent 119894 gainsbased on the field-dependent cognitive style which is definedby the HK model 119888 is the set of cognitive parameters thatrepresents the tendency of an individualrsquos cognitive styleThe value of the cognitive parameter 119888 is the proportionof individual opinion determined by the field-independentcognitive style Therefore 1 - c represents the proportionof individual opinion determined by the field-dependentcognitive style 119888 + 1 minus 119888 = 1 which indicates that individualopinions are codetermined by the two cognitive styles Forexample in the process of marketing our opinions towards aproduct will be influenced by the opinions of our friends andrelatives and wewill also judge the product based on our ownexperience and finally determine our opinions The processof our opinions on the film is similar We are influenced byfilm reviews and we also make judgments based on our field-independent cognition Similarly in the CS model proposedin this paper for each iteration the individual opinion value isupdated according to the individualrsquos own experience (field-independent cognition) and the opinions values of otherneighboring individuals (field-dependent cognition)

3 Numerical Simulations

TheCSmodel was studied by utilizing agent-based modelingand simulations For the sake of convenience we assume thatthe social system is homogeneous meaning that all individ-uals in a given system have the same confidence thresholdand same tendency for cognitive styles Our simulations com-prised 1000 agents in the public opinion evolution systemThe relational network for the agents in the simulation systemwas fully connected which means that any agent could knowthe opinions of all other agents during the evolution ofpublic opinion The reason for selecting a fully connectednetwork was to avoid the effects of network topology onsimulation results The opinions of the agents are quantizedas continuous values between 0 and 1 To avoid the effects ofinitial opinions on the simulation results the initial opinionsof the agents followed a uniform distribution between 0 and1 In the experiments described below we mainly studiedthe influences of the individual field-independent and field-dependent cognitive styles (cognitive parameter 119888) and theinfluence of the individual experience parameter (120596) on theevolution of public opinion in the social system We definethe steady state of the system as follows if the opinion of allindividuals does not continue to change the system becomessteady [56] In addition when the difference between twoopinion values is less than 00001 we regard the two opinionsas the same opinion Two observation indicators were utilizedto measure the impact of these factors on the evolution ofpublic opinion The first is the steady state of the socialsystem which can be represented by the number of opinionclusters when the system reaches a steady state The other issteady time which is how long the system takes to reach asteady state The block diagram of the simulation experimentdesign is shown in Figure 1

Complexity 5

Opinion evolution system

field-independent cognition+

field-dependent cognition

Update opinion value

Start

End

Observation indicatorsof the system

Steady timeSteady state

Experiment AVerify the impact of cognitive

parameter

Experiment BVerify the impact of experience

parameter

Individual initial opinion value

YesNo

Is steady

Figure 1 Block diagram of the simulation experiment design

31 Impact of Field-Independence and Field-Dependence Cog-nitive Styles on Evolution of Public Opinion First we studythe impact of cognitive parameters (119888) on the evolution ofpublic opinion which represents the tendencies of individualcognitive styles In our simulations we consider a constantset of experience parameters (120596 = 05) to facilitate theanalysis of cognitive styles and their influence on publicopinion evolution Figure 2 presents the simulation resultsof the HK model with different confidence thresholds inwhich the X-axis represents the system evolution time andthe Y-axis represents the opinion values of individuals inthe system As shown in Figure 2 for the classical HKmodel with a confidence threshold of 01 there were fourclusters of opinion when the system reached a steady stateWhen the confidence threshold increased to 02 the entiresystem became polarized into two opinion clusters whenit reached a steady state With a confidence threshold of025 all opinions in the social system reached consensus ata steady state Therefore in the HK model the confidencethresholds of 01 02 and 025 correspond to divergencepolarization and consensus respectively which are the threesteady states of the social system In order to study the impactof cognitive styles on public opinion evolution for differentsteady states of a social system we set the confidence thresh-old to values of 120576119894 isin [01 02 021 022 023 024 025]Simultaneously we set the cognitive parameter to values of119888 isin [0 01 02 03 04 05 06 07 08 09]

Figure 3 presents the simulation results for the steadystate of the social systemwith different confidence thresholdsand cognitive parameters (119888) The green yellow and redrectangles represent divergence polarization and consensusrespectively which are the three steady states of the socialsystem When 119888 = 0 the model is equal to the classicalHK model If the confidence threshold is 01 regardlessof the cognitive parameter value the steady state of the

social system is divergence When the confidence thresholdis gradually changed from 02 to 025 the steady state ofthe social system gradually changes from polarization toconsensus One can see that when considering the field-independent cognitive style of individuals the tendency ofthe new model for the steady state of the system to changewith the confidence threshold is similar to that of the classicalHK model As the confidence threshold increases the steadystate of the system changes from divergence to polarizationand eventually reaches consensus However there are differ-ences between the new model and the classical HK modelWhen the confidence threshold is 021 the steady state ofthe system in the classical HK model is consensus but thesteady state of the system considering the field-independentcognitive style is still polarization When the confidencethreshold is 022 the steady state of the system in which thecognitive parameter value was nomore than 05 (119888 le 05) alsochanges to consensus but the steady state of the systemwherethe cognitive parameter value is no less than 06 (119888 ge 06) isstill polarization After the confidence threshold increases to023 except for the steady state of the system in which thecognitive parameter value was no less than 08 (119888 ge 08) thesteady state of the systems has already reached consensusOnce the confidence threshold reaches 024 regardless ofthe cognitive parameter value all steady states of the socialsystems reach consensus Based on the above analysis wecan conclude the value of the cognitive parameter has animpact on the steady state of a social system These resultsalso reveal that the tendencies of individuals toward field-independent and field-dependent cognitive styles have animpact on the evolution of public opinion The larger thevalue of the cognitive parameter (119888) the larger the proportionof individual opinions that are determined by the field-independent cognitive style Specifically individuals aremoreinclined toward the field-independent cognitive style during

6 Complexity

Confidence Threshold01

Confidence Threshold02

Confidence Threshold025

0

01

02

03

04

05

06

07

08

09

1O

pini

on

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

Figure 2 Opinion evolution results for the HK model with different confidence thresholds

0 01 02 03 04 05 06 07 08 09Cognitive parameters c

0102

021022023024025

Con

fiden

ce th

resh

old

Figure 3 Steady state of a social system with different confidencethresholds and cognitive parameters (119888)

the evolution of public opinion whichmakes it more difficultfor the steady state of the social system to reach consensusOnthe contrary the smaller the value of the cognitive parameter119888 the easier it is to reach consensus

To study the influence of cognitive styles on the steadytime of opinion evolution we compare the steady times withdifferent cognitive parameter values for the three steady statesof a social system (divergence polarization and consensus)Asmentioned previously the confidence thresholds we selectare 01 02 and 025 (120576119894 isin [01 02 025]) regardless of thecognitive parameter values the steady state of the social sys-tem always moves toward divergence polarization and con-vergence respectively In the same manner we set the cogni-tive parameter 119888 isin [0 01 02 03 04 05 06 07 08 09] inorder to study the impact of cognitive style on the steady timeof opinion evolution

Figure 4 presents the simulation results for the steadytime of the social system for different values of the cognitiveparameter (119888) for three steady states (divergence polarization

and consensus) When 119888 = 0 the model is equal to theclassical HKmodel One can see fromFigure 4 that comparedto the classical HK model (119888 = 0) the proposed systemrequires a longer time to reach steady state (119888 = 0) It can alsobe seen that irrespective of the steady state of the social system(divergence polarization or convergence) as the value of thecognitive parameter (119888) increases the time required for thesocial system to reach steady state increases This suggeststhat the more the individuals are inclined toward the field-independent cognitive style during the evolution of publicopinion the more time the social system requires to reach asteady state thus stability is more difficult to achieve

Above all we focus on analyzing the impact of thecognitive parameter (119888) on the evolution of public opinionWhen the cognitive parameter is 0 (119888 = 0) only theindividualrsquos field-dependent cognitive style is considered butthe individual field-independent cognitive style is ignoredAt this time the CS model degenerates into the classicalHK model When 119888 = 0 the simulation experimental datareflect the results of the evolution of the classical HK modelCompared with the classical HK model the CS model hasa longer evolution time and it is more difficult to reachconsensus in the system In addition the larger the valueof the cognitive parameter (119888) the greater the proportionof field-independent cognitive styles for individuals Thismeans that individuals have a stronger tendency to followthe field-independent cognitive style during the evolutionof public opinion Thus individuals will focus more oninternal perception and less on external influences whenupdating their own opinions In other words individualsare more likely to perform independent cognition and lesslikely to consider the opinions of their neighbors within theconfidence range However opinion dynamics is a fusion

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

4 Complexity

This is consistent with the concept that individuals updatetheir opinions according to both field-dependence and field-independence in the evolution of public opinion In the fieldof statistical physics as per the model proposed by relevantresearch agents (atoms) change their state based on noiseor temperature (internal characteristics) as well as externalfactors (interaction with neighbors) [54 55] In the processof public opinion evolution the traditional opinion dynamicsmodel (the HK model) only considers the cognitive styleof individual field-dependence it is necessary to introducethe cognitive style of individual field-independence In thismanner the model can bemademore consistent with the realworld

22 CS Model We consider the classical HK model as anexample and consider the field-independent cognitive styleof individuals in this model To construct the HK model weconsider 119899 agents in a system the set of which is denotedas 119873 = 1 2 3 4 119899 where agent 119894 isin 119873 The opinionof agent 119894 at time 119905 is represented by 119909119894(119905) isin (0 1) Initiallyeach agent has an opinion 119909119894(0) where 119909119894(0) isin (0 1)The initial opinions of the agents in the system are subjectto a particular distribution such as a uniform or normaldistribution Each agent has its own threshold of confidence120576119894 When the difference between its opinion and the opinionsof its neighbors is less than the confidence threshold theagent will choose to interact with its neighbors The discrete-time HK model is described by

119909119894 (119905 + 1) =

11003816100381610038161003816119873119894 (119905)

1003816100381610038161003816sum119895isin119873119894(119905)

119909119895 (119905) 119873119894 (119905) = 0

119909119894 (119905) 119900119905ℎ119890119903119908119894119904119890(1)

where 119873119894(119905) = 119895 isin 119881 | |119909119894(119905) minus 119909119895(119905)| le 120576119894 is the opinionneighbor set of agent 119894 at time 119905 and |119873119894(119905)| is the number ofneighbor interactions

When the field-independent cognitive style of individualsis considered in public opinion dynamics we simplify thedefinition of cognition and form a corresponding hypothesisSuppose that during the evolution of public opinion in termsof the field-independent cognitive style the individual willgain opinions only through hisher own experiences Theexperiences of the individual are simplified as opinions inhisher memory and we only consider their opinions at thelast moment in discrete time Therefore we propose a publicopinion evolution model based on cognitive styles (the CSmodel) as described by

119909119894 (119905 + 1) = 119888 sdot [120596 sdot 119909119894 (119905) + (1 minus 120596) sdot 119909119894 (119905 minus 1)] + (1 minus 119888)

sdot 11003816100381610038161003816119873119894

1003816100381610038161003816sum119895isin119873119894

119909119895 (119905)

119873119894 (119905) = 119895 isin 119881 | 10038161003816100381610038161003816119909119894 (119905) minus 119909119895 (119905)10038161003816100381610038161003816 le 120576119894

(2)

120596 sdot 119909119894(119905) + (1 minus 120596) sdot 119909119894(119905 minus 1) is the opinion that agent119894gainsbased on the field-independent cognitive style 120596 is a setof experience parameters that represent the weight of theopinion at time 119905 on the agentrsquos experience (1 minus120596) represents

the weight of the opinion at time 119905 minus 1 on the agentrsquosexperience which is the opinion at the last moment inmemory (1|119873119894|) sum119895isin119873119894 119909119895(119905) is the opinion that agent 119894 gainsbased on the field-dependent cognitive style which is definedby the HK model 119888 is the set of cognitive parameters thatrepresents the tendency of an individualrsquos cognitive styleThe value of the cognitive parameter 119888 is the proportionof individual opinion determined by the field-independentcognitive style Therefore 1 - c represents the proportionof individual opinion determined by the field-dependentcognitive style 119888 + 1 minus 119888 = 1 which indicates that individualopinions are codetermined by the two cognitive styles Forexample in the process of marketing our opinions towards aproduct will be influenced by the opinions of our friends andrelatives and wewill also judge the product based on our ownexperience and finally determine our opinions The processof our opinions on the film is similar We are influenced byfilm reviews and we also make judgments based on our field-independent cognition Similarly in the CS model proposedin this paper for each iteration the individual opinion value isupdated according to the individualrsquos own experience (field-independent cognition) and the opinions values of otherneighboring individuals (field-dependent cognition)

3 Numerical Simulations

TheCSmodel was studied by utilizing agent-based modelingand simulations For the sake of convenience we assume thatthe social system is homogeneous meaning that all individ-uals in a given system have the same confidence thresholdand same tendency for cognitive styles Our simulations com-prised 1000 agents in the public opinion evolution systemThe relational network for the agents in the simulation systemwas fully connected which means that any agent could knowthe opinions of all other agents during the evolution ofpublic opinion The reason for selecting a fully connectednetwork was to avoid the effects of network topology onsimulation results The opinions of the agents are quantizedas continuous values between 0 and 1 To avoid the effects ofinitial opinions on the simulation results the initial opinionsof the agents followed a uniform distribution between 0 and1 In the experiments described below we mainly studiedthe influences of the individual field-independent and field-dependent cognitive styles (cognitive parameter 119888) and theinfluence of the individual experience parameter (120596) on theevolution of public opinion in the social system We definethe steady state of the system as follows if the opinion of allindividuals does not continue to change the system becomessteady [56] In addition when the difference between twoopinion values is less than 00001 we regard the two opinionsas the same opinion Two observation indicators were utilizedto measure the impact of these factors on the evolution ofpublic opinion The first is the steady state of the socialsystem which can be represented by the number of opinionclusters when the system reaches a steady state The other issteady time which is how long the system takes to reach asteady state The block diagram of the simulation experimentdesign is shown in Figure 1

Complexity 5

Opinion evolution system

field-independent cognition+

field-dependent cognition

Update opinion value

Start

End

Observation indicatorsof the system

Steady timeSteady state

Experiment AVerify the impact of cognitive

parameter

Experiment BVerify the impact of experience

parameter

Individual initial opinion value

YesNo

Is steady

Figure 1 Block diagram of the simulation experiment design

31 Impact of Field-Independence and Field-Dependence Cog-nitive Styles on Evolution of Public Opinion First we studythe impact of cognitive parameters (119888) on the evolution ofpublic opinion which represents the tendencies of individualcognitive styles In our simulations we consider a constantset of experience parameters (120596 = 05) to facilitate theanalysis of cognitive styles and their influence on publicopinion evolution Figure 2 presents the simulation resultsof the HK model with different confidence thresholds inwhich the X-axis represents the system evolution time andthe Y-axis represents the opinion values of individuals inthe system As shown in Figure 2 for the classical HKmodel with a confidence threshold of 01 there were fourclusters of opinion when the system reached a steady stateWhen the confidence threshold increased to 02 the entiresystem became polarized into two opinion clusters whenit reached a steady state With a confidence threshold of025 all opinions in the social system reached consensus ata steady state Therefore in the HK model the confidencethresholds of 01 02 and 025 correspond to divergencepolarization and consensus respectively which are the threesteady states of the social system In order to study the impactof cognitive styles on public opinion evolution for differentsteady states of a social system we set the confidence thresh-old to values of 120576119894 isin [01 02 021 022 023 024 025]Simultaneously we set the cognitive parameter to values of119888 isin [0 01 02 03 04 05 06 07 08 09]

Figure 3 presents the simulation results for the steadystate of the social systemwith different confidence thresholdsand cognitive parameters (119888) The green yellow and redrectangles represent divergence polarization and consensusrespectively which are the three steady states of the socialsystem When 119888 = 0 the model is equal to the classicalHK model If the confidence threshold is 01 regardlessof the cognitive parameter value the steady state of the

social system is divergence When the confidence thresholdis gradually changed from 02 to 025 the steady state ofthe social system gradually changes from polarization toconsensus One can see that when considering the field-independent cognitive style of individuals the tendency ofthe new model for the steady state of the system to changewith the confidence threshold is similar to that of the classicalHK model As the confidence threshold increases the steadystate of the system changes from divergence to polarizationand eventually reaches consensus However there are differ-ences between the new model and the classical HK modelWhen the confidence threshold is 021 the steady state ofthe system in the classical HK model is consensus but thesteady state of the system considering the field-independentcognitive style is still polarization When the confidencethreshold is 022 the steady state of the system in which thecognitive parameter value was nomore than 05 (119888 le 05) alsochanges to consensus but the steady state of the systemwherethe cognitive parameter value is no less than 06 (119888 ge 06) isstill polarization After the confidence threshold increases to023 except for the steady state of the system in which thecognitive parameter value was no less than 08 (119888 ge 08) thesteady state of the systems has already reached consensusOnce the confidence threshold reaches 024 regardless ofthe cognitive parameter value all steady states of the socialsystems reach consensus Based on the above analysis wecan conclude the value of the cognitive parameter has animpact on the steady state of a social system These resultsalso reveal that the tendencies of individuals toward field-independent and field-dependent cognitive styles have animpact on the evolution of public opinion The larger thevalue of the cognitive parameter (119888) the larger the proportionof individual opinions that are determined by the field-independent cognitive style Specifically individuals aremoreinclined toward the field-independent cognitive style during

6 Complexity

Confidence Threshold01

Confidence Threshold02

Confidence Threshold025

0

01

02

03

04

05

06

07

08

09

1O

pini

on

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

Figure 2 Opinion evolution results for the HK model with different confidence thresholds

0 01 02 03 04 05 06 07 08 09Cognitive parameters c

0102

021022023024025

Con

fiden

ce th

resh

old

Figure 3 Steady state of a social system with different confidencethresholds and cognitive parameters (119888)

the evolution of public opinion whichmakes it more difficultfor the steady state of the social system to reach consensusOnthe contrary the smaller the value of the cognitive parameter119888 the easier it is to reach consensus

To study the influence of cognitive styles on the steadytime of opinion evolution we compare the steady times withdifferent cognitive parameter values for the three steady statesof a social system (divergence polarization and consensus)Asmentioned previously the confidence thresholds we selectare 01 02 and 025 (120576119894 isin [01 02 025]) regardless of thecognitive parameter values the steady state of the social sys-tem always moves toward divergence polarization and con-vergence respectively In the same manner we set the cogni-tive parameter 119888 isin [0 01 02 03 04 05 06 07 08 09] inorder to study the impact of cognitive style on the steady timeof opinion evolution

Figure 4 presents the simulation results for the steadytime of the social system for different values of the cognitiveparameter (119888) for three steady states (divergence polarization

and consensus) When 119888 = 0 the model is equal to theclassical HKmodel One can see fromFigure 4 that comparedto the classical HK model (119888 = 0) the proposed systemrequires a longer time to reach steady state (119888 = 0) It can alsobe seen that irrespective of the steady state of the social system(divergence polarization or convergence) as the value of thecognitive parameter (119888) increases the time required for thesocial system to reach steady state increases This suggeststhat the more the individuals are inclined toward the field-independent cognitive style during the evolution of publicopinion the more time the social system requires to reach asteady state thus stability is more difficult to achieve

Above all we focus on analyzing the impact of thecognitive parameter (119888) on the evolution of public opinionWhen the cognitive parameter is 0 (119888 = 0) only theindividualrsquos field-dependent cognitive style is considered butthe individual field-independent cognitive style is ignoredAt this time the CS model degenerates into the classicalHK model When 119888 = 0 the simulation experimental datareflect the results of the evolution of the classical HK modelCompared with the classical HK model the CS model hasa longer evolution time and it is more difficult to reachconsensus in the system In addition the larger the valueof the cognitive parameter (119888) the greater the proportionof field-independent cognitive styles for individuals Thismeans that individuals have a stronger tendency to followthe field-independent cognitive style during the evolutionof public opinion Thus individuals will focus more oninternal perception and less on external influences whenupdating their own opinions In other words individualsare more likely to perform independent cognition and lesslikely to consider the opinions of their neighbors within theconfidence range However opinion dynamics is a fusion

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

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[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

Complexity 5

Opinion evolution system

field-independent cognition+

field-dependent cognition

Update opinion value

Start

End

Observation indicatorsof the system

Steady timeSteady state

Experiment AVerify the impact of cognitive

parameter

Experiment BVerify the impact of experience

parameter

Individual initial opinion value

YesNo

Is steady

Figure 1 Block diagram of the simulation experiment design

31 Impact of Field-Independence and Field-Dependence Cog-nitive Styles on Evolution of Public Opinion First we studythe impact of cognitive parameters (119888) on the evolution ofpublic opinion which represents the tendencies of individualcognitive styles In our simulations we consider a constantset of experience parameters (120596 = 05) to facilitate theanalysis of cognitive styles and their influence on publicopinion evolution Figure 2 presents the simulation resultsof the HK model with different confidence thresholds inwhich the X-axis represents the system evolution time andthe Y-axis represents the opinion values of individuals inthe system As shown in Figure 2 for the classical HKmodel with a confidence threshold of 01 there were fourclusters of opinion when the system reached a steady stateWhen the confidence threshold increased to 02 the entiresystem became polarized into two opinion clusters whenit reached a steady state With a confidence threshold of025 all opinions in the social system reached consensus ata steady state Therefore in the HK model the confidencethresholds of 01 02 and 025 correspond to divergencepolarization and consensus respectively which are the threesteady states of the social system In order to study the impactof cognitive styles on public opinion evolution for differentsteady states of a social system we set the confidence thresh-old to values of 120576119894 isin [01 02 021 022 023 024 025]Simultaneously we set the cognitive parameter to values of119888 isin [0 01 02 03 04 05 06 07 08 09]

Figure 3 presents the simulation results for the steadystate of the social systemwith different confidence thresholdsand cognitive parameters (119888) The green yellow and redrectangles represent divergence polarization and consensusrespectively which are the three steady states of the socialsystem When 119888 = 0 the model is equal to the classicalHK model If the confidence threshold is 01 regardlessof the cognitive parameter value the steady state of the

social system is divergence When the confidence thresholdis gradually changed from 02 to 025 the steady state ofthe social system gradually changes from polarization toconsensus One can see that when considering the field-independent cognitive style of individuals the tendency ofthe new model for the steady state of the system to changewith the confidence threshold is similar to that of the classicalHK model As the confidence threshold increases the steadystate of the system changes from divergence to polarizationand eventually reaches consensus However there are differ-ences between the new model and the classical HK modelWhen the confidence threshold is 021 the steady state ofthe system in the classical HK model is consensus but thesteady state of the system considering the field-independentcognitive style is still polarization When the confidencethreshold is 022 the steady state of the system in which thecognitive parameter value was nomore than 05 (119888 le 05) alsochanges to consensus but the steady state of the systemwherethe cognitive parameter value is no less than 06 (119888 ge 06) isstill polarization After the confidence threshold increases to023 except for the steady state of the system in which thecognitive parameter value was no less than 08 (119888 ge 08) thesteady state of the systems has already reached consensusOnce the confidence threshold reaches 024 regardless ofthe cognitive parameter value all steady states of the socialsystems reach consensus Based on the above analysis wecan conclude the value of the cognitive parameter has animpact on the steady state of a social system These resultsalso reveal that the tendencies of individuals toward field-independent and field-dependent cognitive styles have animpact on the evolution of public opinion The larger thevalue of the cognitive parameter (119888) the larger the proportionof individual opinions that are determined by the field-independent cognitive style Specifically individuals aremoreinclined toward the field-independent cognitive style during

6 Complexity

Confidence Threshold01

Confidence Threshold02

Confidence Threshold025

0

01

02

03

04

05

06

07

08

09

1O

pini

on

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

Figure 2 Opinion evolution results for the HK model with different confidence thresholds

0 01 02 03 04 05 06 07 08 09Cognitive parameters c

0102

021022023024025

Con

fiden

ce th

resh

old

Figure 3 Steady state of a social system with different confidencethresholds and cognitive parameters (119888)

the evolution of public opinion whichmakes it more difficultfor the steady state of the social system to reach consensusOnthe contrary the smaller the value of the cognitive parameter119888 the easier it is to reach consensus

To study the influence of cognitive styles on the steadytime of opinion evolution we compare the steady times withdifferent cognitive parameter values for the three steady statesof a social system (divergence polarization and consensus)Asmentioned previously the confidence thresholds we selectare 01 02 and 025 (120576119894 isin [01 02 025]) regardless of thecognitive parameter values the steady state of the social sys-tem always moves toward divergence polarization and con-vergence respectively In the same manner we set the cogni-tive parameter 119888 isin [0 01 02 03 04 05 06 07 08 09] inorder to study the impact of cognitive style on the steady timeof opinion evolution

Figure 4 presents the simulation results for the steadytime of the social system for different values of the cognitiveparameter (119888) for three steady states (divergence polarization

and consensus) When 119888 = 0 the model is equal to theclassical HKmodel One can see fromFigure 4 that comparedto the classical HK model (119888 = 0) the proposed systemrequires a longer time to reach steady state (119888 = 0) It can alsobe seen that irrespective of the steady state of the social system(divergence polarization or convergence) as the value of thecognitive parameter (119888) increases the time required for thesocial system to reach steady state increases This suggeststhat the more the individuals are inclined toward the field-independent cognitive style during the evolution of publicopinion the more time the social system requires to reach asteady state thus stability is more difficult to achieve

Above all we focus on analyzing the impact of thecognitive parameter (119888) on the evolution of public opinionWhen the cognitive parameter is 0 (119888 = 0) only theindividualrsquos field-dependent cognitive style is considered butthe individual field-independent cognitive style is ignoredAt this time the CS model degenerates into the classicalHK model When 119888 = 0 the simulation experimental datareflect the results of the evolution of the classical HK modelCompared with the classical HK model the CS model hasa longer evolution time and it is more difficult to reachconsensus in the system In addition the larger the valueof the cognitive parameter (119888) the greater the proportionof field-independent cognitive styles for individuals Thismeans that individuals have a stronger tendency to followthe field-independent cognitive style during the evolutionof public opinion Thus individuals will focus more oninternal perception and less on external influences whenupdating their own opinions In other words individualsare more likely to perform independent cognition and lesslikely to consider the opinions of their neighbors within theconfidence range However opinion dynamics is a fusion

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

6 Complexity

Confidence Threshold01

Confidence Threshold02

Confidence Threshold025

0

01

02

03

04

05

06

07

08

09

1O

pini

on

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

0

01

02

03

04

05

06

07

08

09

1

Opi

nion

20 30 40 5010Time

Figure 2 Opinion evolution results for the HK model with different confidence thresholds

0 01 02 03 04 05 06 07 08 09Cognitive parameters c

0102

021022023024025

Con

fiden

ce th

resh

old

Figure 3 Steady state of a social system with different confidencethresholds and cognitive parameters (119888)

the evolution of public opinion whichmakes it more difficultfor the steady state of the social system to reach consensusOnthe contrary the smaller the value of the cognitive parameter119888 the easier it is to reach consensus

To study the influence of cognitive styles on the steadytime of opinion evolution we compare the steady times withdifferent cognitive parameter values for the three steady statesof a social system (divergence polarization and consensus)Asmentioned previously the confidence thresholds we selectare 01 02 and 025 (120576119894 isin [01 02 025]) regardless of thecognitive parameter values the steady state of the social sys-tem always moves toward divergence polarization and con-vergence respectively In the same manner we set the cogni-tive parameter 119888 isin [0 01 02 03 04 05 06 07 08 09] inorder to study the impact of cognitive style on the steady timeof opinion evolution

Figure 4 presents the simulation results for the steadytime of the social system for different values of the cognitiveparameter (119888) for three steady states (divergence polarization

and consensus) When 119888 = 0 the model is equal to theclassical HKmodel One can see fromFigure 4 that comparedto the classical HK model (119888 = 0) the proposed systemrequires a longer time to reach steady state (119888 = 0) It can alsobe seen that irrespective of the steady state of the social system(divergence polarization or convergence) as the value of thecognitive parameter (119888) increases the time required for thesocial system to reach steady state increases This suggeststhat the more the individuals are inclined toward the field-independent cognitive style during the evolution of publicopinion the more time the social system requires to reach asteady state thus stability is more difficult to achieve

Above all we focus on analyzing the impact of thecognitive parameter (119888) on the evolution of public opinionWhen the cognitive parameter is 0 (119888 = 0) only theindividualrsquos field-dependent cognitive style is considered butthe individual field-independent cognitive style is ignoredAt this time the CS model degenerates into the classicalHK model When 119888 = 0 the simulation experimental datareflect the results of the evolution of the classical HK modelCompared with the classical HK model the CS model hasa longer evolution time and it is more difficult to reachconsensus in the system In addition the larger the valueof the cognitive parameter (119888) the greater the proportionof field-independent cognitive styles for individuals Thismeans that individuals have a stronger tendency to followthe field-independent cognitive style during the evolutionof public opinion Thus individuals will focus more oninternal perception and less on external influences whenupdating their own opinions In other words individualsare more likely to perform independent cognition and lesslikely to consider the opinions of their neighbors within theconfidence range However opinion dynamics is a fusion

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

Complexity 7

00 02 04 06 08 100

80

160

240

320

400

00 02 04 06 08 10 00 02 04 06 08 100

40

80

120

160

200 ConsensusPolarizationDivergence

Cognitive parameter c

0

40

80

120

160

200St

eady

tim

e

Figure 4 Steady times for the three steady states of the social system (divergence polarization and consensus) for different cognitiveparameters (119888)

process in which individual opinions are based on specificrules [57] When an individual iterates to update hisherown opinion value not only based on hisher neighborsrsquoopinion value but also based on hisher own experience itis equivalent to weakening the influence of hisher neighborsrsquoopinion value on the assimilation of individual opinion valueThis slows down the trend of the unity of group opinionvalue and strengthens the retention of unique opinions in thesystemThus the social system needs a longer time to reach asteady state It alsomeans that the systemhas greater difficultyreaching consensus and is more prone to polarization oreven divergence In the process of public opinion evolutionif the opinion value of the individual is shaped only byneighbors then it is naturally easy to reach consensus butin reality the individual opinion value is not only derivedfromother individuals but also based on internal experienceThus it is difficult for the overall opinion value to becomeconsensus For example in the process of marketing anindividualrsquos opinion on a product depends more on hisherown experience or thinking and less on the reputation ofrelatives and friends Thus hisher opinion is more difficultto change and given the grouprsquos differing opinion on theproduct it is difficult to reach consensus Consider anotherexample where peoplersquos opinions on a film are derived morefrom their own experience or thinking and are less influencedby the film review Therefore it is difficult to agree upon anoverall opinion Considering the field-independent cognitivestyle of the individual the simulation results of public opinionevolution are more realistic Therefore the CS model is animprovement of the classical HK model In addition thevalue of the cognitive parameter (c) reflects the individualrsquostendency to follow the field-independent or field-dependentcognitive style Previous studies have shown that peoplewith different cultural backgrounds have different tendencies

toward these two cognitive styles Therefore the value ofcognitive parameter (c) can be used to represent individualswith different cultural backgrounds The model we proposehere can be used to explore different trends of public opinionevolution in different cultural backgrounds while providinga reference for cross-cultural research

32 Impact of the Experience Parameter (120596) on Evolutionof Public Opinion Next we study the impact of the expe-rience parameter (120596) on the evolution of public opinionSimilar to Section 31 in order to study the impact of theexperience parameter 120596 on the steady state of a socialsystem in our simulations we set the cognitive parame-ter 119888 isin [01 02 03 04 05 06 07 08 09] and changedthe experience parameter 120596 from 0 to 1 Thus 120596 isin[0 01 02 03 04 05 06 07 08 09 1]When the value ofthe experience parameter is zero (120596 = 0) individuals onlyconsider their opinions from the last moment in memorybased on the field-independent cognitive style When thevalue of the experience parameter is one (120596 = 1) individualsdo not consider their opinions from the last moment inmem-ory based on the field-independent cognitive style Thesevalues are the two extremes of the experience parameter 120596

Figure 5 presents the simulation results for the steadystate of the social system with different confidence thresh-olds experience parameters (120596) and cognitive parame-ters (119888) We choose these confidence thresholds (120576119894 isin[021 022 023 024]) because in this case when the valueof the experience parameter (120596) varies the steady state of thesocial system may change based on the value of the cognitiveparameter (119888) Similar to Section 31 the green and yellowrectangles represent consensus and polarization respectivelywhich are the two steady states of the social system As thevalue of the cognitive parameter (119888) increases from 01 to 09

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

8 Complexity

0 05 09 1021

022

023

024

Con

fiden

ce th

resh

old

c=01

0 05 09 1

021

022

023

024

c=02

0 05 1

021

022

023

024

c=03

0 05 1021

022

023

024

Con

fiden

ce th

resh

old

c=04

0 05 1

021

022

023

024

c=05

0 05 09 1

021

022

023

024

c=06

0 05 07 1

021

022

023

024

Con

fiden

ce th

resh

old c=07

0 05 08 1

021

022

023

024

c=08

0 05 1

021

022

023

024

c=09

Experience parameter Experience parameter Experience parameter

Figure 5 Steady state of the social system with different confidence thresholds experience parameters (120596) and cognitive parameters (119888)

the social system requires a larger confidence threshold tochange from polarization to consensus which is consistentwith the results in Section 31 Additionally with the sameconfidence threshold and cognitive parameter (119888) the smallerthe value of the experience parameter (120596) is themore difficultit is for the system to reach consensus When the experienceparameter (120596) is greater than a certain value the systemstate changes from polarization to consensus For examplewith a confidence threshold of 021 and 119888 = 01 the systemstate reaches polarization when the value of the experienceparameter is no more than 08 (120596 le 08) but reachesconsensus when the value of the experience parameter is noless than 09 (120596 ge 09) With a confidence threshold of 022and 119888 = 05 the system state reaches polarization when thevalue of the experience parameter is no more than 04 (120596 le04) but reaches consensus when the value of the experienceparameter is no less than 05 (120596 ge 05) With a confidencethreshold of 023 and 119888 = 08 the system state reachespolarization when the value of the experience parameter isno more than 07 (120596 le 07) but reaches consensus whenthe value of the experience parameter is no more than 08(120596 ge 08) This indicates that the smaller the value of theexperience parameter (120596) is the harder it is for the steadystate of the social system to reach consensus Additionally theimpact of the experience parameter (120596) on the steady state ofthe social system is affected by the cognitive parameter (119888)

Next we study the impact of the experience parameter(120596) on the steady time of opinion evolution One can see fromFigure 5 thatwhen the confidence threshold is 025 regardlessof the value of the cognitive parameter (119888) and experienceparameter (120596) the steady state of the social system alwaysreaches consensus Therefore to maintain a constant steadystate of the social system we select a confidence threshold of025 for our simulation experiments

c=01c=02c=03c=04c=05

c=06c=07c=08c=09

02 04 06 08 1000Experience parameter

0

200

400

Stea

dy ti

me

Figure 6 Steady time with different cognitive parameters (119888) andexperience parameters (120596) and a constant confidence threshold of025

Figure 6 presents the simulation results for steady timewith different experience parameters (120596) and cognitiveparameters (119888) when the steady state of the social systemis always consensus From Figure 6 the time required forthe system to become steady becomes longer as the valueof the cognitive parameter (119888) increases which is consistentwith the previous experiment in Section 31 The lines inFigure 6 generally trend downward which indicates that the

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

Complexity 9

larger the value of the experience parameter (120596) the shorterthe steady time As the value of the cognitive parameter (119888)increases the slopes of the lines become steeper Thereforethe experience parameter (120596) can impact the steady time ofa social system With an increase in the cognitive parameter(119888) the impact on the steady time of the social system is evenstronger

From the above analysis we can conclude that theexperience parameter (120596) has an impact on the steady stateand steady time of a social system When the experienceparameter is 1 (120596 = 1) individuals only use the currentopinions value as the result of field-independent cognitionand do not fully conduct independent field cognition fromtheir experience At this time from the perspective of themodel form the CS model is degraded to the MHK model[27] However in fact individuals are not field-independentcognitively but possess a kind of persistence or confidencein their original opinions Compared with the MHK modelthe CS model takes longer to evolve and the opinion valuesare more difficult to converge Simultaneously the larger thevalue of the experience parameter (120596) is the easier it is forthe steady state of a social system to reach consensus andless time is required for the social system to become steadyThis may be because the larger the value of the experienceparameter (120596) the lower the individual weigh hisher opinionfrom the last moment in memory and the more heshe relieson hisher opinion from the current moment This promotesand accelerates the interaction of individuals with otherindividuals and causes the opinions of individuals to becomeincreasingly biased toward the group opinion Additionallythe larger the value of the cognitive parameter (119888) the greaterthe impact of the experience parameter (120596) on the evolutionof public opinion Individuals become more inclined towardthe field-independent cognitive style and the proportionof their opinions gained via field-independent cognition islarger when they update their opinions This means thatthe impact of experience parameters on the evolution ofpublic opinion is greater Persistence or self-confidence inthe value of onersquos opinion at the last moment is only a copyof onersquos opinion value and cannot be categorized as field-independent cognition of the individual During the evolu-tion of public opinion in reality individual opinions will alsobe based on their own experience which is the function offield-independent cognition of the individual Therefore weuse the experience parameter to construct the independentcognition of individual field which has a realistic basis Aswe all know it is difficult to change the opinions of peoplewho have had certain experiences during the course of theirwork or personal lives For example if an individual is veryexperienced with regard to the storybackground of a film itis difficult to change his opinion Consider another exampleIn the marketing process if a person has experience with aproduct hisher opinion is difficult to change Therefore theresults of our simulation experiment analysis are consistentwith reality

4 Conclusion and Discussion

In this study the field-independent cognitive style of individ-uals was considered in the context of opinion dynamics anda public opinion evolution model based on cognitive styles(the CS model) was proposed In the CS model individualsinvolved in the evolution of public opinion not only changetheir opinions based on the opinions of their neighborsby utilizing a confidence threshold (the field-dependentcognitive style) but also refer to their own experiences(the field-independent cognitive style) By combining thesetwo methods of cognition an individual can update hisheropinion rationally The CS model proposed in this paperwas compared to the classical HK model The simulationresults revealed that the CS model is similar to the clas-sical HK model in some respects For example with anincrease in the confidence threshold the steady state of thesocial system changes from divergence to polarization andeventually reaches consensus The difference is that whenconsidering the field-independent cognition of the individ-ual the individualrsquos opinion value is not only affected byhisher neighbors but also based on hisher own experiencewhich weakens the fusion of group opinions and more likelyretains the unique opinions in the system thus slowing downthe trend of unification of group opinion values Thereforecompared to the classical HK model the state of publicopinion evolution will be more difficult to converge and thetime required for system stability will be longer

Similarly individuals are more inclined to the field-independent cognitive style Thus in the evolution of publicopinion the proportion of opinions values in their ownexperience is larger and the value of neighbors in theconfidence radius is less borrowed which further weakensthe assimilation of neighborsrsquo opinions The influence slowsdown the integration of public opinion as well as the trend ofunification of group opinions As a result the system of publicopinion evolution needs to be stable for a longer period oftime Thus it is more difficult to converge and is more proneto polarization and even divergence The cognitive parameter(119888) and experience parameter (120596) both have an impact onthe steady state and steady time of public opinion evolutionIn the case of larger values for the cognitive parameter (119888)individuals are more inclined toward the field-independentcognitive style meaning the experience parameter (120596) has agreater impact on the evolution of public opinion

If individuals in the public opinion evolution system aremore inclined toward the field-independent cognitive stylethe time required for the system to reach a steady state islonger and the steady state of the system is less likely toreach consensus In contrast if individuals in the publicopinion evolution system are more inclined toward the field-dependent cognitive style the time required for the systemto reach a steady state is shorter and the steady state ofthe system is more likely to reach consensus As mentionedabove the different tendencies of individuals towards thetwo cognitive styles represent two different cultures Peoplein western cultures are more inclined toward the field-independent cognitive style whereas Chinese people aremore inclined toward the field-dependent cognitive style It

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

10 Complexity

is well-known that policymaking in certain western countriesis slow and difficult [58 59] For example gun controlpolicies in the United States where many people are killedby firearms every year have been difficult to pass [60]There are many reasons for this and it represents a scenariowhere public opinion has difficulty reaching a steady stateof consensus Similarly perhaps because of cultural reasonsChinese people tend to be influenced by the opinions ofthe people around them and public opinion evolves quicklyoften easily reaching consensus inChinese societyThus cultsof personality are more likely to develop in China [61ndash63]These real-world examples are consistent with our simulationresults Therefore the consideration of the field-independentcognitive style in opinion dynamics models not only is morerealistic but also serves as a basis for cross-cultural research

In this paper we simplified the cognitive style of indi-vidual field-independence by examining only the individualexperience dimension In future research we will considerthe field-independent cognitive style of individuals in opin-ion dynamics in additional dimensions to make our modelricher and more realistic

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 71571081 In additionShen Zhao expresses heartfelt thanks to his father and hisgirlfriend Jing Liu for their help and support over the years

References

[1] P Burnstein ldquoThe impact of public opinion on public policy areview and agendardquo Political Research Quarterly vol 56 no 1pp 29ndash40 2003

[2] N Breznau andHAndreszligPublic Opinion and Social Policy as aFeedback System fromTheory to Empirical Model SpecificationSocial Science Electronic Publishing 2016

[3] T W Moore P D Finley J M Lineberger et al ExtendingOpinion Dynamics to Model Public Health Problems andAnalyze Public Policy Interventions 2011

[4] X Chen X Xiong M Zhang and W Li ldquoPublic authoritycontrol strategy for opinion evolution in social networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 26no 8 Article ID 083105 2016

[5] R Hegselmann and U Krause ldquoOpinion dynamics andbounded confidence models analysis and simulationrdquo Journalof Artificial Societies amp Social Simulation vol 5 no 3 p 2 2002

[6] C Yin X Huang Y Chen S Dadras S-M Zhong and YCheng ldquoFractional-order exponential switching technique to

enhance sliding mode controlrdquo Applied Mathematical Mod-elling Simulation and Computation for Engineering and Envi-ronmental Systems vol 44 pp 705ndash726 2017

[7] C Yin X Huang S Dadras et al ldquoDesign of optimal light-ing control strategy based on multi-variable fractional-orderextremum seeking methodrdquo Information Sciences vol 465 pp38ndash60 2018

[8] C Yin S Dadras X Huang J Mei H Malek and Y ChengldquoEnergy-saving control strategy for lighting system basedon multivariate extremum seeking with Newton algorithmrdquoEnergy Conversion andManagement vol 142 pp 504ndash522 2017

[9] S Dadras ldquoPath tracking using fractional order extremumseek-ing controller for autonomous ground vehiclerdquo SAE TechnicalPapers 2017-01-0094 2017

[10] S Dadras S Dadras H Malek and Y Chen ldquoA note on thelyapunov stability of fractional-order nonlinear systemsrdquo inProceedings of the ASME 2017 International Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference American Society ofMechanical EngineersUSA 2017

[11] S Dadras S Dadras andHMomeni ldquoLinear matrix inequalitybased fractional integral sliding-mode control of uncertainfractional-order nonlinear systemsrdquo Journal of Dynamic Sys-tems Measurement and Control vol 139 no 11 Article ID111003 2017

[12] J R P French Jr ldquoA formal theory of social powerrdquoPsychologicalReview vol 63 no 3 pp 181ndash194 1956

[13] R A Holley and T M Liggett ldquoErgodic theorems for weaklyinteracting infinite systems and the voter modelrdquo Annals ofProbability vol 3 no 4 pp 643ndash663 1975

[14] S Galam ldquoMinority opinion spreading in random geometryrdquoThe European Physical Journal B - Condensed Matter andComplex Systems vol 25 no 4 pp 403ndash406 2002

[15] S Bikhchandani D Hirshleifer and I Welch ldquoLearning fromthe behavior of others conformity fads and informationalcascadesrdquo Journal of Economic Perspectives (JEP) vol 12 no 3pp 151ndash170 1998

[16] K Sznajd-Weron and J Sznajd ldquoOpinion evolution in closedcommunityrdquo International Journal of Modern Physics C vol 11no 6 pp 1157ndash1165 2000

[17] G Deffuant D Neau F Amblard and G Weisbuch ldquoMixingbeliefs among interacting agentsrdquoAdvances in Complex Systems(ACS) vol 3 no 01-04 pp 87ndash98 2000

[18] J Lorenz ldquoContinuous opinion dynamics under boundedconfidence a surveyrdquo International Journal of Modern PhysicsC vol 18 no 12 pp 1819ndash1838 2007

[19] JM Olson andM P Zanna ldquoA new look at selective exposurerdquoJournal of Experimental Social Psychology vol 15 no 1 pp 1ndash151979

[20] M Pineda R Toral and E Hernandez-Garcıa ldquoDiffusingopinions in bounded confidence processesrdquo The EuropeanPhysical Journal D vol 62 no 1 pp 109ndash117 2011

[21] X Chen X Zhang Z Wu H Wang G Wang and W LildquoOpinion evolution in different social acquaintance networksrdquoChaos An Interdisciplinary Journal of Nonlinear Science vol 27no 11 Article ID 113111 11 pages 2017

[22] G Sebastian and J Pablo ldquoOpinion group formation anddynamics Structures that last fromnonlasting entitiesrdquoPhysicalReview E Statistical Nonlinear and Soft Matter Physics vol 85no 6 Article ID 066113 2012

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

Complexity 11

[23] M Pineda R Toral and E Hernandez-Garcıa ldquoThe noisyHegselmann-Krause model for opinion dynamicsrdquo The Euro-pean Physical Journal B vol 86 no 12 article no 490 2013

[24] J Lorenz ldquoHeterogeneous bounds of confidence meet discussand find consensusrdquo Complexity vol 15 no 4 pp 43ndash52 2010

[25] J Su B Liu Q Li et al ldquoCoevolution of opinions and directedadaptive networks in a social grouprdquo Journal of ArtificialSocieties amp Social Simulation vol 17 no 2 p 4 2014

[26] J M Su B H Liu Q Li et al ldquoTrust evolution and consensusof opinions in a social grouprdquo Acta Physica Sinica vol 63 no 5pp 71ndash76 2014

[27] G Fu W Zhang and Z Li ldquoOpinion dynamics of modi-fied Hegselmann-Krause model in a group-based populationwith heterogeneous bounded confidencerdquo Physica A StatisticalMechanics and its Applications vol 419 pp 558ndash565 2015

[28] S Chen D H Glass and M McCartney ldquoCharacteristics ofsuccessful opinion leaders in a bounded confidence modelrdquoPhysica A Statistical Mechanics and its Applications vol 449pp 426ndash436 2016

[29] Y Zhang Q Liu S Zhang and L Wang ldquoOpinion formationwith time-varying bounded confidencerdquo Plos One vol 12 no 3Article ID e0172982 2017

[30] ldquoCognition - definition of cognition in English from the Oxforddictionaryrdquo 2016 httpswwwoxforddictionariescom

[31] H A Witkin ldquoA cognitive-style approach to cross-culturalresearchrdquo International Journal of Psychology vol 2 no 4 pp233ndash250 1967

[32] D R Goodenough H A Witkin H B Lewis D Koulack andH Cohen ldquoRepression interference and field dependence asfactors in dream forgettingrdquo Journal of Abnormal Psychologyvol 1973 no 2 pp 32ndash44 1974

[33] H A Witkin and D R Goodenough ldquoField dependence andinterpersonal behaviorrdquoPsychological Bulletin vol 84 no 4 pp661ndash689 1977

[34] D R Goodenough ldquoThe role of individual differences in fielddependence as a factor in learning and memoryrdquo PsychologicalBulletin vol 83 no 4 pp 675ndash694 1976

[35] F P McKenna ldquoMeasures of field dependence Cognitivestyle or cognitive abilityrdquo Journal of Personality and SocialPsychology vol 47 no 3 pp 593ndash603 1984

[36] W Linden ldquoPracticing of meditation by school children andtheir levels of field dependence-independence test anxietyand reading achievementrdquo Journal of Consulting and ClinicalPsychology vol 41 no 1 pp 139ndash143 1973

[37] R J Riding and V A Dyer ldquoExtraversion field-independenceand performance on cognitive tasks in twelve-year-old chil-drenrdquo Journal of Research in Education vol 29 no 1 pp 1ndash91983

[38] B M Frank and D Keene ldquoThe effect of learnersrsquo field inde-pendence cognitive strategy instruction and inherent word-listorganization on free-recallmemory and strategy userdquo Journal ofExperimental Education vol 62 no 1 pp 14ndash25 1993

[39] C Tinajero and M F Paramo ldquoField dependence-inde-pendence and academic achievement A re-examination of theirrelationshiprdquo British Journal of Educational Psychology vol 67no 2 pp 199ndash212 1997

[40] C Angeli ldquoExamining the effects of field dependence-inde-pendence on learnersrsquo problem-solving performance and inter-action with a computer modeling tool Implications for thedesign of joint cognitive systemsrdquo Computers amp Education vol62 pp 221ndash230 2013

[41] P Engelbrecht and S G Natzel ldquoCultural variations in cognitivestyle Field dependence vs field independencerdquo School Psychol-ogy International vol 18 no 2 pp 155ndash164 1997

[42] M McCool and K St Amant ldquoField dependence and classifi-cation implications for global information systemsrdquo Journal ofthe Association for Information Science and Technology vol 60no 6 pp 1258ndash1266 2014

[43] A Mirtabatabaei and F Bullo ldquoOn opinion dynamics inheterogeneous networksrdquo in Proceedings of the 2011 AmericanControl Conference ACC 2011 pp 2807ndash2812 USA 2011

[44] X Chen X Zhang Y Xie et al ldquoOpinion dynamics of social-similarity-based hegselmannndashkrause modelrdquo Complexity vol2017 Article ID 1820257 12 pages 2017

[45] D Pellegreno and F Stickle ldquoField-dependencefield-independence and labeling of facial affectrdquo Perceptual andMotor Skills vol 48 no 2 pp 489-490 1979

[46] L Tascon M Boccia L Piccardi and J M CimadevillaldquoDifferences in spatial memory recognition due to cognitivestylerdquo Frontiers in Pharmacology vol 8 p 550 2017

[47] B M Frank ldquoFlexibility of information processing and thememory of field-independent and field-dependent learnersrdquoJournal of Research in Personality vol 17 no 1 pp 89ndash96 1983

[48] M A Guisande C T Vacas F Cadaveira et al ldquoAttentionand visuospatial abilities a neuropsychological approach infield-dependent and field-independent schoolchildrenrdquo StudiaPsychologica vol 54 no 2 pp 83ndash94 2012

[49] M A Guisande M F Paramo C Tinajero and L S AlmeidaldquoField dependence-independence (FDI) cognitive style Ananalysis of attentional functioningrdquo Psicothema vol 19 no 4pp 572ndash577 2007

[50] H Gintis ldquoStrong reciprocity and human socialityrdquo Journal ofTheoretical Biology vol 206 no 2 pp 169ndash179 2000

[51] P A Tao and X Tong ldquoGovernance of mass disturbance whichcaused by NIMBYrdquo Nanjing Journal of Social Sciences 2010

[52] J M Paige ldquoPolitical orientation and riot participationrdquo Amer-ican Sociological Review vol 36 no 5 pp 810ndash820 1971

[53] R C Eberhart Swarm Intelligence 2001[54] H E Stanley ldquoSpherical model as the limit of infinite spin

dimensionalityrdquo Physical Review A Atomic Molecular andOptical Physics vol 176 no 2 pp 718ndash722 1968

[55] E Ising ldquoBeitrag zur theorie des ferromagnetismusrdquo Zeitschriftfur Physik vol 31 no 1 pp 253ndash258 1925

[56] H Liang Y Yang and X Wang ldquoOpinion dynamics in net-works with heterogeneous confidence and influencerdquo PhysicaA Statistical Mechanics and its Applications vol 392 no 9 pp2248ndash2256 2013

[57] Y Dong X Chen H Liang and C-C Li ldquoDynamics oflinguistic opinion formation in bounded confidence modelrdquoInformation Fusion vol 32 pp 52ndash61 2016

[58] M Fischer Reactive Slow and Innovative Decision-makingStructures and Policy Outputs Palgrave Macmillan UK 2015

[59] M L Volcansek ldquoJudges courts and policy-making inWesternEuroperdquoWest European Politics vol 15 no 3 pp 1ndash8 1992

[60] The Lancet ldquoGun deaths and the gun control debate in theUSArdquoThe Lancet vol 390 no 10105 p 1812 2017

[61] T Flew and L Yin ldquoXi Dada loves Peng Mama digital cultureand the return of charismatic authority in ChinardquoThesis Elevenvol 144 no 1 pp 80ndash99 2018

12 Complexity

[62] L R Luqiu ldquoThe Reappearance of the Cult of Personality inChinardquo East Asia vol 33 no 4 pp 1ndash19 2016

[63] Y Wang ldquoThe formation mechanism of deified personality cultofMao Zedongrsquos and reflection from the perspective of culturalpsychologyrdquo Social Sciences Journal of Universities in Shanxi2015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom