Symbiosis Evolution of Science Communication Ecosystem

Research ArticleSymbiosis Evolution of Science Communication EcosystemBased on SocialMedia A LotkandashVolterraModel-Based Simulation

Ming Xia 1 Xiangwu He 2 and Yubin Zhou 1

1School of Economics and Management Tongji University Shanghai 200092 China2Business School Jiaxing University Jiaxing 314001 China

Correspondence should be addressed to Yubin Zhou dazhoutongjieducn

Received 15 December 2020 Revised 27 February 2021 Accepted 1 April 2021 Published 15 April 2021

Academic Editor Jiaojiao Jiang

Copyright copy 2021 Ming Xia et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Social media has become an important way for science communication Some scholars have examined how to help scientistsengage with social media from operational training policy guidance and social media services improving +e main contributionof this study is to construct a symbiosis evolution model of science communication ecosystem (SCE) between scientists and socialmedia platforms based on the symbiosis theory and the LotkandashVolterra model to discuss the evolution of their symbiotic patternsand population size under different symbiosis coefficients +e results indicate that (1) the size of the symbiosis coefficientsdetermines the equilibrium outcome of the symbiosis evolution of scientists and social media platforms (2) scientists and socialmedia platforms can promote each otherrsquos population size under the mutualism pattern which can achieve sustainable sciencecommunication (3) ldquo1 + 1gt 2rdquo effect can only be achieved under the symmetric mutualism pattern and the growth of scientistsand social media platforms is more stable and sufficient than that of other patterns +e findings will provide additionalperspectives for promoting the sustainable development of science communication based on social media

1 Introduction

+e communication between scientists and the public ischanging as we enter the information age It is a fact of masscommunication effect research that exposure is a necessarycondition for media effect and that communication activitiesoften fail due to insufficient exposure [1] +e rapid de-velopment of new media such as social media has broughttremendous changes to the technological environment ofscience communication [2] It has become one of the mostinfluential factors in science communication and the studyof media as an environmental factor has become a researchhotspot [3]

Social media has dramatically changed the ecologicalenvironment of science communication +e traditionalform of media essentially disseminates information from asingle point to the target audience [4] +e emergence ofsocial media has created a domain-based electronic com-munity that facilitates information interaction [5 6] Inaddition to changing the way information is disseminated

shortening the temporal and spatial distance between thepublic and the scientific community and creating conditionsfor public participation in scientific research changes in thetechnological environment have more importantly enrichedthe vector of dissemination of scientific information Sincethe publication of Robert Hookrsquos micrographs images havebeen placed at the center of the modern science commu-nication process [7] In the era of digital communicationtechnological advances have enriched the transmissionmedium of science and technology information +e de-velopment of video images virtual reality augmented re-ality and mixed reality technology has created a visualinformation-intensive environment for science communi-cation and greatly expanded the dimension of interactionbetween experts and the public [8]

In recent years recognizing the enormous potential ofthe changing technological environment at the level ofknowledge exchange and knowledge diffusion the academiccommunity has begun to experiment with the use of socialmedia as a way to communicate their academic ideas to the

HindawiComplexityVolume 2021 Article ID 6655469 12 pageshttpsdoiorg10115520216655469

public [9] +rough the use of social media in the process ofacademic research social media has become structurallyembedded in the scholarly communication system [10]Scholars have confirmed the possibility of using social mediafor scientific research [11 12] Previous research hasestablished that researchers can build connections andconduct academic exchanges through social media andobtain new research ideas from them and there is evidenceof a positive trend in this kind of use [13ndash15] Howeverstatistics show that most scientists have yet to use socialmedia such as Facebook Twitter WeChat and Weibo intheir professional or academic work [16] Collins et al (2012)surveyed a large number of scholars from the US and UK onthe use of social media and found that 3 of them are highlyactive on Twitter [17] +ese data are far from the 23 ofAmerican adult users owned by Twitter and 71 ofAmerican adult users owned by Facebook +is gap alsoshows that the habit of using social media in academicworkplaces has not yet been developed [18]

+erefore what prevents scientists from using socialmedia to engage in science communication Most scholarsbelieve that scientists are supposed to be dedicated to theirresearch not to the promotion of their findings on socialmedia and that the dissemination of science through themedia results in the undermining of scientistsrsquo authority[19] ldquoSagan Effectrdquo has been used to describe scientists wholdquorisk the contempt of serious scientists by becoming sciencecommunicatorsrdquo +e bias can be roughly summed up asscientists who are diligent in science communication aresecond-rate scientists [20] After the gradual development ofscience communication more scientists have emerged toparticipate in science communication but the ldquoSagan Effectrdquostill influences scientistsrsquo choices Besides it has been shownthat some scientists are fearful of using social media due to alack of knowledge about the usage of social media privacyand other considerations which leads to knowledge barriersat the level of ability to use social media [21] ldquoLack of timerdquois another important influencing factor time wastage hasbeen identified as an important barrier to scientistsrsquo outreach[22] in the field of science communication the use of socialmedia is considered a waste of time by some researchers[23 24] as well as the lack of general clarity on the benefits ofparticipating in social media and the fact that social mediathemselves are at odds with scientific rigor make socialmedia unattractive to scientists [25]

Further how to help scientists use social media Collinset al (2016) advocate guiding scientists to engage with socialmedia by conducting professional development trainingworkshops or a more explicit departmental social media usepolicy [26] Training usually includes helping scientists findand clarify their message learning to work with mediaprofessionals and preparing for the use of social media[27ndash29] +e science communication training program hasdeveloped rapidly in recent years it emphasizes technicalcommunication skills and guides scientists to find theircommunication opportunities Exemplars of programs in-clude Alan Alda Center for Communicating Science theCenter for Public Engagement with Science and Technologyat the American Association for the Advancement of

Science COMPASS and the Portal to the Public Network[30 31] From the perspective of social media platformssome scholars have studied the service upgrades made bysocial media platforms to attract scientists and other contentcreators [32] To be an attractive platform for users (espe-cially content creators) social media offers a variety offeatures such as allowing users to create their channelspostcontent that can be immediately shared with a wideaudience choose to become friends with others or subscribeto other channels and then comment on or choose thecontent what you like [33] Features provide an incentive forcontent creators including scientists Also content creatorscan share revenue generated by user donations through theplatform which supports social media to ensure its inno-vation and long-term viability [34] +e scale effect of socialmedia can attract more content creators to participate inscience communication [35] Similarly as a major force ofscience communication the increase in the number ofgroups of scientists is indicative of a strong user demand thatcan lead to more niche social media-based science com-munication platforms [36 37] +ere is a symbiosis rela-tionship between scientists and social media platforms andthe population numbers between scientists and social mediaplatforms influence each other

In summary scholars have researched the current sit-uation of scientistsrsquo participation in social media the reasonsfor the lack of participation vitality and the measures thatshould be taken and have achieved relatively rich results Areview of the literature reveals that existing research mainlyfocuses on the individual level of scientists and social mediaplatforms Scholars hope to achieve compatibility betweenscientists and social media on individual changes therebyenhancing the vitality of scientists to participate in socialmedia From an ecological point of view scientists and socialmedia platforms as two symbiotic units in the sciencecommunication ecosystem (SCE) are symbiosis relation-ship and a change in the population size of one will have animpact on the population size of the other inevitably In thisstudy we discuss the population symbiosis between scien-tists and social media platforms from an ecological per-spective establish a LotkandashVolterra population competitionmodel between scientists and social media platforms andinvestigate the symbiosis evolution between them withdifferent symbiosis coefficients under a certain environ-mental carrying capacity to complement the research aboutscientistsrsquo use of social media for sustainable sciencecommunication

+e remainder of this study is mainly divided into thefollowing sections Section 2 is preliminary Section 3 in-troduces the symbiosis evolution model of the SCE based onthe LotkandashVolterra model Sections 4 and 5 are simulationanalyses and conclusions respectively

2 Preliminary

21 Symbiosis (eory +e concept ldquosymbiosisrdquo is of Greekorigin and was first introduced by the German mycologistAnto de Bary in 1879 to refer to the concept of differentgenera living together in an extended material relationship

2 Complexity

[38] Symbiosis is a self-organizing phenomenon and theneed for survival between living organisms is inevitablyinterdependent and interactive in some way forming asymbiosis relationship of coexistence and synergistic evo-lution [39] However the concept of symbiosis has not yetbeen harmonized due to the influence of different disci-plinary contexts Symbiosis in the narrower sense is con-sidered as a reciprocal mutually beneficial cooperativerelationship between species +e German scientist Buchnerconsidered symbiosis to be an intimate enduring unionbetween two dissimilar organisms and tended to limit it to amutually beneficial union [40] Dale Weis defines symbiosisas a stable enduring and intimate combined relationshipbetween several pairs of cooperators [41] In a broad sensesymbiosis is the existence of power relationships betweenspecies such as metabolism and energy conversion Mar-gulis an American biologist pointed out from an ecologicalpoint of view that ldquosymbiosis is the union of important partsof the life cycles of individuals of different speciesrdquo [39] Goff(1982) pointed out that symbiosis includes various degrees ofparasitism commensalism and mutualism [38]

Based on the symbiosis theory Yuan (1998) discussedthe three elements symbiotic units symbiotic patterns andsymbiotic environment [42] +e symbiotic units are thebasic units of energy production and exchange that con-stitute the symbiosis relationship which is the basis for theexistence of the symbiosis relationship the symbiotic pat-tern also known as the symbiosis relationship is the form ofinteraction or combination of symbiotic units which reflectsnot only the pattern of action between the symbiotic unitsbut also the intensity of action which reflects the exchangeof material information between the symbiotic units as wellas the exchange of energy between the symbiotic units thesymbiotic environment refers to the exogenous conditionsfor the development of the existence of the symbiotic pat-tern and the sum of all factors other than the symbiotic unitsconstitute the symbiotic environment which is the guar-antee for the survival of the symbiotic units +ree elementsare indispensable as shown in Figure 1

22 Structure of SCE SCE based on social media is acomplex system composed of multiple individual usersgathered on a certain type of social media platform andformed by the interconnection and influence of its externalnetwork environment and the real social environmentSimilar to the natural ecosystem the SCE has a continuousevolutionary process from creation expansion maintenanceto decline +e structure is an important indicator of thebalance and sustainability of an ecosystem [43 44] +estructure of the SCE refers to the combination of the rel-atively stable interaction patterns of various componentsand the internal manifestations of their temporal and spatialrelationships +is study focuses on the analysis of thesymbiosis relationship between scientists and social mediaplatforms in terms of the ecological chain structure of theSCE and the flow of information resources

+e ecological chain structure of the ecosystem mainlyrefers to the network structure formed by the chain network

between biological components [45] Take natural ecosys-tems as an example Although natural ecosystems varygreatly in appearance structure and feature each naturalecosystem has three main elements producers consumersand decomposers and realizes the smooth flow of matterand energy through the above three main elements [46 47]+e SCE belongs to the category of the social ecosystem butit still has the relevant elements of the natural ecosystem+ese similarities are manifested in the similar ecologicalchain structure of the natural ecosystem and the scienceecosystem but they are still different as shown in Figure 2

+e natural ecological chain is composed of producersmultilevel consumers and decomposers Producers andprimary consumers primary consumers and secondaryconsumers form an ecological sequence through the preyingrelationship Producers and consumers involved in each linkof energy flow are decomposed and released into the en-vironment again to form a closed loop of energy flow

+e difference between the science communicationecological chain and the natural ecological chain is mainlyreflected in the changes in the relationship between pro-ducers and consumers +e relationship between producersand consumers in the natural ecological chain is predationEnergy flow is a one-way flow from producers to consumers[48] However there is no traditional ldquopredationrdquo rela-tionship between scientists and the public in the sciencecommunication ecological chain or the meaning of ldquopre-dationrdquo has been transformed into a two-way symbiosisrelationship between scientistsrsquo access to public attentionand the publicrsquos access to knowledge from scientists Sci-entists and social media platforms social media platformsand the public form a symbiosis relationship through theflow of information and because of the addition of a two-way adjustment mechanism with feedback the way of in-formation flow has also changed from one-way to two-wayand the positive direction of information flow represents theprocess of scientific communication and reverse flow rep-resents the process of information consultation andfeedback

3 Methodology

+is section will introduce the background and developmentstatus of the LotkandashVolterra model at first and then build amodel of the symbiosis evolution of SCE based on theLotkandashVolterra model considering the specific context of theissue Finally we will discuss the different symbiosis rela-tionships under different symbiosis coefficients and thestable conditions at this time

31 LotkandashVolterra Model In this paper the authors at-tempt to explore the symbiosis and evolution of scientistsand social media platforms in the SCE with computersimulation methods +e SCE based on social media is anecosystem composed of scientific communities social mediaplatforms users and so on +is study draws on the eco-logical evolution method to explore the number structureand overall evolution of its internal population From an

Complexity 3

ProducePrimary

consumersSecondaryconsumers

Inorganic reduction

Prey on Decompose

Decompose

Scientist Social media Public

Informationtransfer

Recycle

Feedback

ldquoBidirectional predation relationshiprdquo

Science communication ecological chain

ldquoSymbiosisrdquoldquoSymbiosisrdquo

Nature ecological chain

Prey on

Informationtransfer

Information recycling

Decomposer

Recycler

Figure 2 Comparison between nature ecological chain and science communication ecological chain +e direction of the arrow indicatesthe direction of information or energy flow and the dashed line indicates the relationship between the two sides

Symbioticunit 1

Symbioticinterface

Compatible

Compatible

Newenergy Newen

ergy

Newen

ergy

NewenergyPattern 1

Pattern 2

External environment

Internal environment

Evolution

Evolution Evolutio

n

Evolut

ion

Symbioticunit 2

Symbioticunit 3

Symbioticunit 4

Transform

TransformTransform

Transform

Figure 1 Symbiosis evolution of symbiotic units +e symbiotic units exchange energy and information through quality parameters on thesymbiotic interface and the new energy generated changes the symbiosis pattern and gradually realizes the symbiosis evolution

4 Complexity

ecological point of view the growth and change law ofbiological populations is as follows in a short periodgenerally follow the Malthus model growth law that is thepopulation size grows exponentially with the growth oftime the population size gradually increases the influence ofdensity constraints is increasing and showing the logisticgrowth law and the growth rate of population size becomesslower and gradually reaches saturation +e differentialequation expression is shown in model

dN(t)

dt αN(t) 1 minus

N(t)

Nlowast1113888 1113889 (1)

In model (1) suppose that there is one population in theecosystem under a certain natural growth rate α +epopulation size N(t) will gradually change over time andreach the maximum population size Nlowastin a specific envi-ronment eventually +e logistic model was first applied tothe estimation of population and then it was widely used inpopulation ecology and sociology [49]

+e LotkandashVolterra model is proposed by Lotka andVolterra based on a single species logistic model whichconsiders the dynamic growth of two or more populations inthe ecosystem at the same time [50] as shown in model

dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δN2(t)

Nlowast2

1113888 1113889 (2)

In model (2) suppose that there are two populations inthe ecosystem under a certain natural growth rate α1 +epopulation size of each species is affected not only by the sizeof its population but also by the size of another population+e population size N1(t) will gradually change over timeand reach the maximum population size Nlowast1 in a specificenvironment eventually

LotkandashVolterra model has good data fitting andprediction performance and is widely used in research invarious fields such as economics business urbanizationand sociology In economic research Bernardo andDrsquoAlessandro (2016) studied a macroeconomic frame-work based on the LotkandashVolterra model to assess thesocial and economic consequences of investing in low-carbon options [51] In business research Khan et al(2018) studied the impact of low-cost airlines on Koreanfull-service companies and tourism based on the Lot-kandashVolterra model [52] In the urbanization researchAssumma et al (2019) discussed how to use the systemdynamics model and the LotkandashVolterra model to assessregional elasticity [53] In sociological research Marascoand Romano (2018) used LotkandashVolterra to study theintergenerational conflicts in the American aging societyfrom 1974 to 2014 [54] Ditzen (2018) studied the mul-tinational convergence of the LotkandashVolterra model [55]Christodoulakis (2016) used the dynamic LotkandashVolterramodel to quantitatively analyze the armed confrontationthat occurred in Greece from 1946 to 1949 and explainedthe dynamics and costs of the conflict in the Greek CivilWar [56]

32 Analysis of the Symbiosis Evolution

321 Hypothesis

Hypothesis 1 +ere is a certain number of scientists andsocial media platforms in the SCE +e population of sci-entists and social media platforms is affected by factors suchas policy economy society infrastructure technologyscientific research environment and science communicationindustry environment

Hypothesis 2 Changes in the scale of scientists and socialmedia platforms in the social media ecology reflect theirrespective growth conditions +e positive change in thepopulation size indicates the use of various science resourcesin the SCE +e higher the degree the greater the gainsobtained during the evolution of the symbiosis relationshipand the better the growth the reverse change of the pop-ulation size indicates that the population has a low degree ofutilization of various scientific resources in the SCE in thecontext of science communication and the symbiosis re-lationship is evolving +e income obtained is low and thegrowth of the population is poor When the utilization rateof a population for popular science resources is 0 it indicatesthat the population is extinct

Hypothesis 3 +e growth process of the group of scientistsand social media platforms obeys the logistic growth lawDue to the limitation of the capacity of the ecosystem thepopulation growth rate when each participant grows alonewill gradually decrease as the population density increases

Hypothesis 4 When the marginal output of the populationof scientists or social media platforms equals the marginalinput the population growth rate tends to 0 and thepopulation reaches its maximum size

322 Symbiosis Evolution Model Assume that the twogroups grow independently and do not affect each other Wesuppose that the population numbers of scientists and socialmedia platforms are N1 and N2 and the natural growth ratesare α1 and α2 respectively Nlowast1 and Nlowast2 are here used to referto the maximum size of the two types of the populationunder the given resource elements +e dynamic evolutionequations of the two types of symbiotic units in the SCE canbe expressed as equation group

dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

1113890 1113891

N1(0) N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

1113890 1113891

N2(0) N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Complexity 5

In the equation group (3) the initial size of the pop-ulation of scientists and social media organizations in socialmedia networks is N10 and N20 respectively α1N1(t) andα2N2(t) are used here to refer to reflect the number ofscientists participating in social media and the developmenttrend of the population of social media platforms1 minus (N1(t)Nlowast1 ) and 1 minus (N2(t)Nlowast2 ) are the logistic coef-ficient which is used here to refer to the hindrance of thegrowth of their scale due to the consumption of limitedresources by the two types of participants respectively

Considering the interaction between populations andaccording to the symbiosis theory the two types of symbioticunits will undergo a transition from one symbiosis pattern toanother during the development process embodying dif-ferent symbiosis effects and forming different symbiosisrelationships [57] When two types of symbiotic units in-teract in the SCE the growth of each type of symbiotic unit isnot only affected by its population size but also related to thepopulation size of the other type of symbiotic unitsAccording to the LotkandashVolterra model the symbiosis co-efficient δ is here introduced to reflect the size of thesymbiosis effect Based on this the dynamic model of theinteraction and evolution of the population of social mediascientists and social media organizations can be expressed asequation group

dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

In equation group (4) δ12 and δ21 are symbiosis coef-ficient which is used here to indicate the symbiosis effect ofscientists participating in social media on the population sizeof social media organizations and social media organizationson the population size of scientists participating in socialmedia +at is the changes of the quality parameter of theother party caused by the interaction between the qualityparameters N1(t) and N2(t) δ21(N2(t)Nlowast2 ) andδ12(N1(t)Nlowast1 ) indicate the degree of influence caused byboth parties and the values of δ12 and δ21 reflect the sym-biotic pattern of the two types of symbiosis units in the SCE

323 Model Analysis According to the different valueranges of δ12and δ21 the LotkandashVolterra model of the in-teraction of the two types of symbiotic units and theirsymbiosis relationship is discussed in Table 1

It can be seen that the result of the symbiosis evolutionbetween the group of scientists and social media organi-zations in the SCE depends on the value of the symbiosiscoefficient To study the symbiosis evolution relationshipbetween scientists and social media organizations it isnecessary to analyze the equilibrium point and stabilityconditions of the dynamic evolution equation and analyzethe symbiosis evolution results of the two types of symbioticunits When (dN1(t)dt) 0 and (dN2(t)dt) 0 the fourlocal equilibrium points of the symbiosis evolution of dif-ferent symbiosis units in the social media ecological networkcan be obtained namely E1(0 0) E2(Nlowast1 0) E3(0 Nlowast2 ) andE4((Nlowast1(1 minus δ21)1 minus δ21δ12) (Nlowast2(1 minus δ12)1 minus δ12)) For theSCE described by a system of differential equations toparticipate in the evolution of the subject the stability of itsequilibrium point can be obtained by analyzing the localstability of the Jacobian matrix Taking the partial derivativesof N1and N2for the differential equations in turn the Ja-cobian matrix of the symbiosis evolution between scientistsand social media organizations in the SCE can be obtained asequation (5)

J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)

+e method of using the Jacobian matrix to judgewhether the equilibrium point is locally asymptotically stableis as follows when the system equilibrium point makesdet(J)gt 0 and tr(J)lt 0 then it is a stable equilibrium pointAt this time the equilibrium point is in a locally progressiveand stable state +erefore in the SCE the conditions for thesymbiosis evolution between the group of scientists andsocial media organizations are det(J)gt 0 and tr(J)lt 0 +especific analysis results are shown in Table 2

4 Results and Discussion

41 Simulation Analysis +e two types of symbiotic unitsscientists and social media platforms adopt a division oflabor and cooperation to create new value generate newlyavailable resources promote the evolution of symbiosisrelationships expand the scale of the SCE through the reuseof resources and improve the operational efficiency of theSCE +is study uses MATLAB2019a to simulate the

6 Complexity

differential equations (3) to explore how the community ofscientists and social media platforms interact and evolvesymbiosis under different values of δ12 and δ21 as shown in

dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

α1N1(t) 1 minusN1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)

+is paper uses the fourth-fifth-order RungendashKutta al-gorithm to solve the numerical problem It is assumed thatthe natural growth rates of the population of scientistsparticipating in social media and the social media platformsare α1 002 and α2 001 respectively the maximumgrowth scale of the two types of symbiosis units isNlowast1 Nlowast2 100 when resources and environment allowthe iteration period is set to 1000 and the simulation resultsare shown in Figures 3ndash8

(1) Independent coexistence Figure 3 shows the sim-ulation results of the two types of symbiotic units inthe SCE under the independent coexistence patternAt this time there is no symbiosis relationship be-tween them and the symbiosis coefficient betweenthe scientist and the social media platform is 0 Inthis pattern the growth rate of the two types ofsymbiotic units does not affect each other and thegrowing scale is only affected by its growth rate Inthe independent coexistence pattern the stableequilibrium point is (Nlowast1 Nlowast2 ) that is when the two

types of symbiotic units are in equilibrium theirgrowth scale reaches the upper limit +is patterngenerally exists in the early stage of the formation ofthe SCE Science communication activities not onlyare related to startups but also involve various en-tities in the system +erefore this pattern is veryrare short-lived and unstable

Table 1 +e value range of the symbiosis coefficient and its corresponding symbiosis pattern δ21 represents the influence coefficient of thescale change of population 2 on the growth of population 1

Value range Symbiosispattern Feature

δ12 0 δ21 0 Not symbiosis Two symbiotic units developed independentlyδ12 gt 0 δ21 gt 0 Not symbiosis Two symbiotic units compete maliciouslyδ12 lt 0 δ21 gt 0 orδ12 gt 0 δ21 lt 0

Parasitic Two types of symbiotic units one reduced (δgt 0) and the other benefited (δ lt 0)

δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0

Commensalism Two types of symbiotic units one that benefits (δlt 0) and the other that does not affect(δ 0)

δ12 lt 0 δ21 lt 0 Mutualism Asymmetric mutualism between two types of symbiotic units (δ12 ne δ21) symmetricmutualism between two types of symbiotic units (δ12 δ21)

Table 2 Equilibrium and stability condition of SCE

Equilibrium det(J) tr(J) Stabilitycondition

E1(0 0) α1α2 α1 + α2 UnstableE2(Nlowast1 0) minus α1α2(1 minus δ12) minus α1 + α2(1 minus δ12) δ12 gt 1E3(0 Nlowast2 ) minus α1α2(1 minus δ21) minus α2 + α1(1 minus δ21) δ21 gt 1E4((Nlowast1(1 minus δ21)1 minus δ21δ12)(Nlowast2(1 minus δ12)1 minus δ12))

(α1α2(δ21 minus 1)(δ12 minus 1)1 minus δ21δ12) (α1(δ21 minus 1) + α2(δ12 minus 1)1 minus δ21δ12) δ21 lt 1 δ12 lt 1

α1 = 002 α2 = 001δ12 = 00 δ21 = 00

ScientistsSocial media

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times

Figure 3 Independent coexistence pattern Changes in the size ofthe two populations after 1000 iterations ( α1 002 α2 001δ12 0 and δ21 0)

Complexity 7

(2) Competitive coexistence In the evolution of the SCEanother pattern that does not exist in symbiosis iscompetition and coexistence As shown in Figure 4the symbiosis coefficient between the scientist groupand the social media platform at this time is greaterthan 0 the symbiosis coefficient of the participating

social media scientists on the social media platform isgreater than 1 and the stable equilibrium point is(Nlowast1 0) +is pattern may exist when scientists havebetter resources and technology from other chan-nels Social media platforms tend to decline due tothe consumption of a large number of resources andthe group of scientists has survived However due tomutual competition the group of scientists has alsosuffered losses and it is difficult to exceed themaximum scale under its constraints Nlowast1

(3) Parasitic coexistence Figure 5 shows the simulationresults of the parasitic symbiosis pattern of two typesof symbiotic units in the SCE In this pattern thesocial media platforms have a positive symbiosiseffect on the group of scientists participating in itwhile the group of scientists cannot give equalreturns to the social media platforms and cause anegative symbiosis effect on it 0lt δ12 lt 1 and δ21 lt 0the stable equilibrium point at this time is((Nlowast1(1 minus δ21)1 minus δ21δ12) (Nlowast2(1 minus δ12)1 minus δ12)) Itcan be seen that the upper limit of the growth scale ofthe scientist population under equilibrium condi-tions exceeds its maximum growth scale Nlowast1 +esocial media platform has declined due to the con-sumption of the resources of the scientists partici-pating in social media and the growth scale is farbelow themaximum scaleNlowast2 At the same time withthe advancement of science communication activi-ties the scale of the group of scientists participatingin social media has gradually expanded Althoughthe parasitic behavior of the group of scientists has


α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

Figure 4 Competitive coexistence pattern Changes in the size ofthe two populations after 1000 iterations ( α1 002 α2 001δ12 01 and δ21 02)

Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


Figure 5 Parasitic coexistence pattern Changes in the size of thetwo populations after 1000 iterations ( α1 002α2 001 δ12 02 and δ21 minus 01)


α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e

Figure 6 Commensalism pattern Changes in the size of the twopopulations after 1000 iterations ( α1 002 α2 001 δ12 0and δ21 minus 01)

8 Complexity

hindered the development of social media platformsit has not formed a fatal threat and the growth ofsocial media platforms has been stable at a certainvalue below its maximum growth scale At this time

the benefits of ldquo1 + 1gt 2rdquo have not been realizedbetween symbiotic units and both of them needmore resource interaction and value sharing topromote symbiosis evolution

(4) Commensalism As shown in Figure 6 in this pat-tern one of the symbiosis coefficients between thesocial media platform and the participating scientistsis less than zero and the other is equal to zero +estable equilibrium point at this time is(Nlowast1(1 minus δ21) Nlowast2 ) +e benefits brought by thesymbiosis relationship made up for the damage thatthe social media platform suffered in the parasiticsymbiosis pattern and its growth scale returned tothe maximum quality parameter Nlowast2 of independentgrowth+e group of scientists participating in socialmedia continues to benefit through symbiosis rela-tionships beyond the maximum growth scale Nlowast1when growing up independently Under the com-mensalism pattern the group of scientists continuedto obtain technical capital and equipment supportfrom the social media platform and graduallyreturned profits talents services and content tocompensate for the prerequisite investment of thesocial media platforms +e two types of symbioticunits get through the most difficult period for sciencecommunication and transit into the growth phase

(5) Asymmetric mutualism Figure 7 shows the simu-lation results of the asymmetric mutualism betweenscientists participating in social media and socialmedia platforms +e symbiosis coefficients of thetwo types of symbiosis units are both less than 0 butnot equal +e stable equilibrium point at this timeis ((Nlowast1(1 minus δ21)1 minus δ21δ12) (Nlowast2(1 minus δ12)1 minus δ12))+e growth scale of the two types of symbiotic unitsexceeds the maximum scale of independent de-velopment under the constraints of their respectiveresources and environments +e upper limit of thesize of each symbiotic unit is related to the sym-biosis coefficient +e greater the absolute value ofthe symbiosis coefficient the higher the upper limitof its growth scale At the same time with thewithdrawal of funds and technologies from socialmedia platforms there are more options to choosefrom and the growth momentum is accelerating Atthis time the evolution of the SCE has graduallyentered a mature stage and the symbiosis rela-tionship between scientists participating in socialmedia and social media platforms has begun toenter a win-win pattern

(6) Symmetric mutualism Symmetric mutualism is thehighest level pursued in the process of symbiosisevolution As shown in Figure 8 the symbiosis co-efficients of the two types of symbiotic units are bothless than zero and equal +e growth scale of the twotypes of symbiotic units not only exceeds the max-imum quality parameter of independent develop-ment but also tends to be consistent In themutualism pattern scientists involved in social


α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times

Figure 7 Asymmetric mutualism pattern Changes in the size ofthe two populations after 1000 iterations ( α1 002 α2 001δ12 minus 01 and δ21 minus 02)


α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times

Figure 8 Symmetric mutualism pattern Changes in the size of thetwo populations after 1000 iterations ( α1 002 α2 001δ12 minus 01 and δ21 minus 01)

Complexity 9

media have close cooperation mutual promotionand mutual dependence on social media platforms+ey have a good coordination mechanism and aresource sharing mechanism and ultimately achieveldquo1 + 1gt 2rdquo economic benefits

From the above analysis it can be concluded that theSCE based on social media is a complex system formed bythe symbiosis and evolution of scientists and social mediaplatforms +e coefficient of symbiosis between scientistsparticipating in social media and social media platformsdetermines the result of the evolution of the system differentsymbiosis relationships will eventually lead to differentevolution directions and eventually reach an equilibriumstate +e two types of symbiosis units under the mutuallybeneficial symbiosis pattern have the largest growth ratewhich is the best direction for the evolution of social mediaecological symbiosis

5 Conclusions

+is study summarized the concept of the SCE based on theactual situation discussed the symbiosis evolution rela-tionship between scientists and social media platforms in theSCE based on the LotkandashVolterra model within the theo-retical framework of symbiosis theory and calculated theequilibrium point and stability conditions of the symbiosisevolution with the Jacobian matrix Comparing the sym-biosis evolution pattern under different coefficients we gotsome important conclusions as follows

(1) +e SCE in the context of science communication iscomposed of symbiotic units including scientists and socialmedia platforms and interacts through different symbiosispatterns under the influence of economic policy and cul-tural symbiosis environments Eventually a self-organizingadaptive coordination system is formed +e process ofsystem integration is bound to go through stages of for-mation growth and maturity +e symbiosis relationshipbetween the group of scientists and social media platformswill directly affect the development of the SCE (2) +esymbiosis coefficient between scientists and social mediadetermines the equilibrium result of the symbiosis andevolution of the SCE Independent coexistence competitivecoexistence parasitic coexistence and commensalism can-not promote the virtuous circle of the SCE only if under themutualism pattern scientists and social media platformspromote each otherrsquos population size which can achievesustainable science communication (3) +e SCE based onsocial media can only produce economic benefits ofldquo1 + 1gt 2rdquo under the symmetric mutualism pattern +egrowth of scientists and social media organizations underthe symmetric mutualism pattern is more stable andabundant than that of other patterns

Generally subsequent research can be carried out fromthe following aspects (1) Introduce the research results ofthis study into specific practical situations for analysis Forexample we could conduct an empirical analysis of thenumber of scientists participating in social media for sci-entific communication and the number of social media

platforms during a period to make a useful supplement tothe simulation results (2) Explore the evolution of the SCEunder the symbiosis organization mode and discuss how itevolves from point symbiosis intermittent symbiosis andcontinuous symbiosis to integrated symbiosis (3) Refer tothe existing research on complex systems explore thecompetition and cooperation mechanism and metabolismmechanism in the SCE and provide corresponding sug-gestions for more effectively promoting the virtuous circle ofscience communication

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is study was supported by the National Natural ScienceFoundation of China (no 71972148)

References

[1] F El Kihal I Abouelkheir M Rachik and I Elmouki ldquoRoleof media and effects of infodemics and escapes in the spatialspread of epidemics a stochastic multi-region model withoptimal control approachrdquo Mathematics vol 7 2019

[2] A Orben ldquoTeenagers screens and social media a narrativereview of reviews and key studiesrdquo Social Psychiatry andPsychiatric Epidemiology vol 55 no 4 pp 407ndash414 2020

[3] J Maier and B Rittberger ldquoShifting europersquos boundariesrdquoEuropean Union Politics vol 9 no 2 pp 243ndash267 2008

[4] C Puschmann ldquoAnalyzing political communication withdigital trace data the role of twitter messages in social scienceresearchrdquo Information Communication amp Society vol 19no 12 pp 1691-1692 2015

[5] D Sgroi ldquoSocial network theory broadband and the future ofthe World Wide Webrdquo Telecommunications Policy vol 32no 1 pp 62ndash84 2008

[6] A I Cristea D Katsaros and Y Manolopoulos ldquoIntroduc-tion to the special issue of the world wide web journal onldquosocial media preservation and applicationsrdquordquo World WideWeb vol 17 no 4 pp 691ndash693 2014

[7] C Leppanen D M Frank J J Lockyer et al ldquoMedia rep-resentation of hemlock woolly adelgid management risks acase study of science communication and invasive speciescontrolrdquo Biological Invasions vol 21 no 2 pp 615ndash624 2018

[8] P Hunter ldquo+e growth of social media in sciencerdquo EMBOReports p 21 2020

[9] V Cheplygina F Hermans C Albers N Bielczyk andI Smeets ldquoTen simple rules for getting started on Twitter as ascientistrdquo Plos Comput Biol vol 16 Article ID e10075132020

[10] C R Sugimoto S Work V Lariviere and S HausteinldquoScholarly use of social media and altmetrics a review of theliteraturerdquo Journal of the Association for Information Scienceand Technology vol 68 no 9 pp 2037ndash2062 2017

10 Complexity

[11] X Lu C W Phang and J Yu ldquoEncouraging participation invirtual communities through usability and sociability devel-opmentrdquo ACM SIGMIS Database (e DATABASE for Ad-vances in Information Systems vol 42 no 3 pp 96ndash114 2011

[12] S Choi H Lee and Y Yoo ldquo+e impact of informationtechnology and transactive memory systems on knowledgesharing application and team performance a field studyrdquoMis Quarterly vol 34 no 4 pp 855ndash870 2010

[13] A Gruzd K Staves and A Wilk ldquoConnected scholars ex-amining the role of social media in research practices offaculty using the UTAUT modelrdquo Computers in HumanBehavior vol 28 no 6 pp 2340ndash2350 2012

[14] R B Lee R Baring M S Maria and S Reysen ldquoAttitudetowards technology social media usage and grade-pointaverage as predictors of global citizenship identification inFilipino University Studentsrdquo International Journal of Psy-chology vol 52 no 3 pp 213ndash219 2017

[15] C Tenopir R Volentine and D W King ldquoSocial media andscholarly readingrdquo Online Information Review vol 37 no 2pp 193ndash216 2013

[16] E C M Parsons D S Shiffman E S Darling N Spillmanand A J Wright ldquoHow Twitter literacy can benefit conser-vation scientistsrdquo Conservation Biology vol 28 no 2pp 299ndash301 2014

[17] K Collins D Shiffman and J Rock ldquoHow are scientists usingsocial media in the workplacerdquo PLoS One vol 11 Article IDe0162680 2016

[18] J Juenger and B Faehnrich ldquoDoes really no one care ana-lyzing the public engagement of communication scientists onTwitterrdquo New Media amp Society vol 22 pp 387ndash408 2019

[19] B Faehnrich and C Luthje ldquoRoles of social scientists in crisismedia reporting-the case of the German populist radical rightmovement PEGIDArdquo Science Communication vol 39pp 415ndash442 2017

[20] X Liang L Y-F Su S K Yeo et al ldquoBuilding buzzrdquoJournalism amp Mass Communication Quarterly vol 91 no 4pp 772ndash791 2014

[21] J M Heemstra ldquoA scientistrsquos guide to social mediardquo ACSCentral Science vol 6 no 1 pp 1ndash5 2020

[22] I Rowlands D Nicholas B Russell N Canty andA Watkinson ldquoSocial media use in the research workflowrdquoLearned Publishing vol 24 no 3 pp 183ndash195 2011

[23] B Beck-Winchatz ldquoInvolvement of scientists in the NASAOffice of Space Science education and public outreach pro-gramrdquo Nuclear Physics B - Proceedings Supplements vol 138pp 451ndash453 2005

[24] C Stylinski and A Johnson ldquoImpacts of a comprehensivepublic engagement training and support programrdquo Interna-tional Journal of Science Education vol 4 no 8 pp 340ndash3542018

[25] A T Taylor and S M Sammons ldquoBridging the gap betweenscientists and anglers the black bass conservation committeersquossocial media outreach effortsrdquo Fisheries vol 44 no 1pp 37ndash41 2019

[26] J T H Wang C J Power C M Kahler et al ldquoCommu-nication ambassadors-an Australian social media initiative todevelop communication skills in early career scientistsrdquoJournal of Microbiology amp Biology Education vol 19 2018

[27] B Smith N Baron C English et al ldquoCOMPASS navigatingthe rules of scientific engagementrdquo PLoS Biology vol 11Article ID e1001552 2013

[28] K D Heath E Bagley A J M Berkey et al ldquoAmplify thesignal graduate training in broader impacts of scientific re-searchrdquo BioScience vol 64 no 6 pp 517ndash523 2014

[29] A Baram-Tsabari and B V Lewenstein ldquoScience commu-nication training what are we trying to teachrdquo InternationalJournal of Science Education Part B vol 7 no 3 pp 285ndash3002017

[30] C Stylinski M Storksdieck N Canzoneri E Klein andA Johnson ldquoImpacts of a comprehensive public engagementtraining and support program on scientistsrsquo outreach attitudesand practicesrdquo International Journal of Science EducationPart B vol 8 no 4 pp 340ndash354 2018

[31] E Salas S I Tannenbaum K Kraiger and K A Smith-Jentsch ldquo+e science of training and development in orga-nizationsrdquo Psychological Science in the Public Interest vol 13no 2 pp 74ndash101 2012

[32] J Wan Y Lu B Wang and L Zhao ldquoHow attachmentinfluences usersrsquo willingness to donate to content creators insocial media a socio-technical systems perspectiverdquo Infor-mation amp Management vol 54 no 7 pp 837ndash850 2017

[33] A Susarla J-H Oh and Y Tan ldquoSocial networks and thediffusion of user-generated content evidence from YouTuberdquoInformation Systems Research vol 23 no 1 pp 23ndash41 2012

[34] S Krishnamurthy and A K Tripathi ldquoMonetary donations toan open source software platformrdquo Research Policy vol 38no 2 pp 404ndash414 2009

[35] Q K Mahmood S R Jafree and M M Sohail ldquoPakistaniyouth and social media addiction the validation of bergenFacebook addiction scale (BFAS)rdquo International Journal ofMental Health and Addiction 2020

[36] M Kaakinen A Sirola I Savolainen and A OksanenldquoShared identity and shared information in social mediadevelopment and validation of the identity bubble rein-forcement scalerdquo Media Psychology vol 23 no 1 pp 25ndash512018

[37] B B Dedeoglu B Taheri F Okumus and M GannonldquoUnderstanding the importance that consumers attach tosocial media sharing (ISMS) scale development and valida-tionrdquo Tourism Management p 76 2020

[38] L J GOFF ldquoSymbiosis and parasitism another viewpointrdquoBioScience vol 32 no 4 pp 255-256 1982

[39] D Leidner ldquoReview and theory symbiosis an introspectiveretrospectiverdquo Journal of the Association for InformationSystems vol 19 no 06 pp 552ndash567 2018

[40] L Vancurova V Kalnıkova O Peksa et al ldquoSymbiosis be-tween river and dry lands phycobiont dynamics on rivergravel barsrdquo Algal Research p 51 2020

[41] P Kerdlap J S C Low and S Ramakrishna ldquoLife cycleenvironmental and economic assessment of industrial sym-biosis networks a review of the past decade of models andcomputational methods through a multi-level analysis lensrdquo(e International Journal of Life Cycle Assessment vol 25no 9 pp 1660ndash1679 2020

[42] J Zhang and W L Chen ldquo+e study on integration of supplychain based on the symbiosis theoryrdquo Applied Mechanics andMaterials vol 275-277 pp 2706ndash2709 2013

[43] G Fontaine M-A Maheu-Cadotte A Lavallee et alldquoCommunicating science in the digital and social mediaecosystem scoping review and typology of strategies used byhealth scientistsrdquo JMIR Public Health and Surveillance vol 5no 3 p e14447 2019

[44] K M Meyer A M Hopple A M Klein A H MorrisS D Bridgham and B J M Bohannan ldquoCommunitystructure - ecosystem function relationships in the CongoBasin methane cycle depend on the physiological scale offunctionrdquo Molecular Ecology vol 29 no 10 pp 1806ndash18192020

Complexity 11

[45] M Loreau ldquoCoexistence of multiple food chains in a het-erogeneous environment interactions among communitystructure ecosystem functioning and nutrient dynamicsrdquoMathematical Biosciences vol 134 no 2 pp 153ndash188 1996

[46] X Tan W Qin G Tang C Xiang and X Liu ldquoModels toassess the effects of nonsmooth control and stochastic per-turbation on pest control a pest-natural-enemy ecosystemrdquoComplexity vol 2019 14 pages 2019

[47] P Wang W Qin and G Tang ldquoModelling and analysis of ahost-parasitoid impulsive ecosystem under resource limita-tionrdquo Complexity vol 2019 12 pages 2019

[48] J-L Uso-Domenech J-A Nescolarde-Selva M Lloret-Cli-ment H Gash and K Alonso-Stenberg ldquoIndirect effectsbiotic inferential interactions and time functions in H-se-miotic systems ecosystems caserdquo Mathematics vol 7 2019

[49] A Voroshilova and J Wafubwa ldquoDiscrete competitive lot-kandashvolterra model with controllable phase volumerdquo Systemsvol 8 2020

[50] S Guo and S Yan ldquoHopf bifurcation in a diffusive Lotka-Volterra type system with nonlocal delay effectrdquo Journal ofDifferential Equations vol 260 no 1 pp 781ndash817 2016

[51] G Bernardo and S DrsquoAlessandro ldquoSystems-dynamic analysisof employment and inequality impacts of low-carbon in-vestmentsrdquo Environmental Innovation and Societal Transi-tions vol 21 pp 123ndash144 2016

[52] N T Khan Y H Kim and Y B Kim ldquo+e dynamic impact oflow-cost carriers on full-service carriers and the tourismindustry of South Korea a competitive analysis using theLotka-Volterra modelrdquo Asia Pacific Journal of Tourism Re-search vol 23 no 7 pp 656ndash666 2018

[53] V Assumma M Bottero G Datola E De Angelis andR Monaco ldquoDynamic models for exploring the resilience interritorial scenariosrdquo Sustainability vol 12 2019

[54] A Marasco and A Romano ldquoDeterministic modeling inscenario forecasting estimating the effects of two publicpolicies on intergenerational conflictrdquo Quality amp Quantityvol 52 no 5 pp 2345ndash2371 2017

[55] J Ditzen ldquoCross-country convergence in a general Lotka-Volterra modelrdquo Spatial Economic Analysis vol 13 no 2pp 191ndash211 2017

[56] N Christodoulakis ldquoConflict dynamics and costs in the GreekCivil war 1946-1949rdquo Defence and Peace Economics vol 27no 5 pp 688ndash717 2015

[57] G Faye and M Holzer ldquoAsymptotic stability of the criticalpulled front in a Lotka-Volterra competition modelrdquo Journalof Differential Equations vol 269 no 9 pp 6559ndash6601 2020

12 Complexity

public [9] +rough the use of social media in the process ofacademic research social media has become structurallyembedded in the scholarly communication system [10]Scholars have confirmed the possibility of using social mediafor scientific research [11 12] Previous research hasestablished that researchers can build connections andconduct academic exchanges through social media andobtain new research ideas from them and there is evidenceof a positive trend in this kind of use [13ndash15] Howeverstatistics show that most scientists have yet to use socialmedia such as Facebook Twitter WeChat and Weibo intheir professional or academic work [16] Collins et al (2012)surveyed a large number of scholars from the US and UK onthe use of social media and found that 3 of them are highlyactive on Twitter [17] +ese data are far from the 23 ofAmerican adult users owned by Twitter and 71 ofAmerican adult users owned by Facebook +is gap alsoshows that the habit of using social media in academicworkplaces has not yet been developed [18]

+erefore what prevents scientists from using socialmedia to engage in science communication Most scholarsbelieve that scientists are supposed to be dedicated to theirresearch not to the promotion of their findings on socialmedia and that the dissemination of science through themedia results in the undermining of scientistsrsquo authority[19] ldquoSagan Effectrdquo has been used to describe scientists wholdquorisk the contempt of serious scientists by becoming sciencecommunicatorsrdquo +e bias can be roughly summed up asscientists who are diligent in science communication aresecond-rate scientists [20] After the gradual development ofscience communication more scientists have emerged toparticipate in science communication but the ldquoSagan Effectrdquostill influences scientistsrsquo choices Besides it has been shownthat some scientists are fearful of using social media due to alack of knowledge about the usage of social media privacyand other considerations which leads to knowledge barriersat the level of ability to use social media [21] ldquoLack of timerdquois another important influencing factor time wastage hasbeen identified as an important barrier to scientistsrsquo outreach[22] in the field of science communication the use of socialmedia is considered a waste of time by some researchers[23 24] as well as the lack of general clarity on the benefits ofparticipating in social media and the fact that social mediathemselves are at odds with scientific rigor make socialmedia unattractive to scientists [25]

Further how to help scientists use social media Collinset al (2016) advocate guiding scientists to engage with socialmedia by conducting professional development trainingworkshops or a more explicit departmental social media usepolicy [26] Training usually includes helping scientists findand clarify their message learning to work with mediaprofessionals and preparing for the use of social media[27ndash29] +e science communication training program hasdeveloped rapidly in recent years it emphasizes technicalcommunication skills and guides scientists to find theircommunication opportunities Exemplars of programs in-clude Alan Alda Center for Communicating Science theCenter for Public Engagement with Science and Technologyat the American Association for the Advancement of

Science COMPASS and the Portal to the Public Network[30 31] From the perspective of social media platformssome scholars have studied the service upgrades made bysocial media platforms to attract scientists and other contentcreators [32] To be an attractive platform for users (espe-cially content creators) social media offers a variety offeatures such as allowing users to create their channelspostcontent that can be immediately shared with a wideaudience choose to become friends with others or subscribeto other channels and then comment on or choose thecontent what you like [33] Features provide an incentive forcontent creators including scientists Also content creatorscan share revenue generated by user donations through theplatform which supports social media to ensure its inno-vation and long-term viability [34] +e scale effect of socialmedia can attract more content creators to participate inscience communication [35] Similarly as a major force ofscience communication the increase in the number ofgroups of scientists is indicative of a strong user demand thatcan lead to more niche social media-based science com-munication platforms [36 37] +ere is a symbiosis rela-tionship between scientists and social media platforms andthe population numbers between scientists and social mediaplatforms influence each other

In summary scholars have researched the current sit-uation of scientistsrsquo participation in social media the reasonsfor the lack of participation vitality and the measures thatshould be taken and have achieved relatively rich results Areview of the literature reveals that existing research mainlyfocuses on the individual level of scientists and social mediaplatforms Scholars hope to achieve compatibility betweenscientists and social media on individual changes therebyenhancing the vitality of scientists to participate in socialmedia From an ecological point of view scientists and socialmedia platforms as two symbiotic units in the sciencecommunication ecosystem (SCE) are symbiosis relation-ship and a change in the population size of one will have animpact on the population size of the other inevitably In thisstudy we discuss the population symbiosis between scien-tists and social media platforms from an ecological per-spective establish a LotkandashVolterra population competitionmodel between scientists and social media platforms andinvestigate the symbiosis evolution between them withdifferent symbiosis coefficients under a certain environ-mental carrying capacity to complement the research aboutscientistsrsquo use of social media for sustainable sciencecommunication

+e remainder of this study is mainly divided into thefollowing sections Section 2 is preliminary Section 3 in-troduces the symbiosis evolution model of the SCE based onthe LotkandashVolterra model Sections 4 and 5 are simulationanalyses and conclusions respectively

2 Preliminary

21 Symbiosis (eory +e concept ldquosymbiosisrdquo is of Greekorigin and was first introduced by the German mycologistAnto de Bary in 1879 to refer to the concept of differentgenera living together in an extended material relationship

2 Complexity








3 Methodology



Complexity 3

ProducePrimary


Inorganic reduction

Prey on Decompose

Decompose


Informationtransfer

Recycle

Feedback





Prey on

Informationtransfer


Decomposer

Recycler


Symbioticunit 1

Symbioticinterface

Compatible

Compatible

Newenergy Newen

ergy

Newen

ergy

NewenergyPattern 1

Pattern 2



Evolution

Evolution Evolutio

n

Evolut

ion

Symbioticunit 2

Symbioticunit 3

Symbioticunit 4

Transform

TransformTransform

Transform


4 Complexity


dN(t)

dt αN(t) 1 minus

N(t)

Nlowast1113888 1113889 (1)



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δN2(t)

Nlowast2

1113888 1113889 (2)




321 Hypothesis






dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

1113890 1113891

N1(0) N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

1113890 1113891

N2(0) N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Complexity 5



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)




6 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity








3 Methodology



Complexity 3

ProducePrimary


Inorganic reduction

Prey on Decompose

Decompose


Informationtransfer

Recycle

Feedback





Prey on

Informationtransfer


Decomposer

Recycler


Symbioticunit 1

Symbioticinterface

Compatible

Compatible

Newenergy Newen

ergy

Newen

ergy

NewenergyPattern 1

Pattern 2



Evolution

Evolution Evolutio

n

Evolut

ion

Symbioticunit 2

Symbioticunit 3

Symbioticunit 4

Transform

TransformTransform

Transform


4 Complexity


dN(t)

dt αN(t) 1 minus

N(t)

Nlowast1113888 1113889 (1)



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δN2(t)

Nlowast2

1113888 1113889 (2)




321 Hypothesis






dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

1113890 1113891

N1(0) N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

1113890 1113891

N2(0) N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Complexity 5



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)




6 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity

ProducePrimary


Inorganic reduction

Prey on Decompose

Decompose


Informationtransfer

Recycle

Feedback





Prey on

Informationtransfer


Decomposer

Recycler


Symbioticunit 1

Symbioticinterface

Compatible

Compatible

Newenergy Newen

ergy

Newen

ergy

NewenergyPattern 1

Pattern 2



Evolution

Evolution Evolutio

n

Evolut

ion

Symbioticunit 2

Symbioticunit 3

Symbioticunit 4

Transform

TransformTransform

Transform


4 Complexity


dN(t)

dt αN(t) 1 minus

N(t)

Nlowast1113888 1113889 (1)



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δN2(t)

Nlowast2

1113888 1113889 (2)




321 Hypothesis






dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

1113890 1113891

N1(0) N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

1113890 1113891

N2(0) N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Complexity 5



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)




6 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity


dN(t)

dt αN(t) 1 minus

N(t)

Nlowast1113888 1113889 (1)



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δN2(t)

Nlowast2

1113888 1113889 (2)




321 Hypothesis






dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

1113890 1113891

N1(0) N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

1113890 1113891

N2(0) N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Complexity 5



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)




6 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity



dN1(t)

dt α1N1(t) 1 minus

N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113890 1113891

N1 t0( 1113857 N10

dN2(t)

dt α2N2(t) 1 minus

N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113890 1113891

N2 t0( 1113857 N20

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)




J

α1 1 minus 2N1(t)

Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889 minus α1δ21N1(t)

Nlowast2

minus α2δ12N2(t)

Nlowast1

α2 1 minus 2N2(t)

Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(5)




6 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity


dN1(t)

dt

dN2(t)

dt

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦


Nlowast1

minus δ21N2(t)

Nlowast2

1113888 1113889


Nlowast2

minus δ12N1(t)

Nlowast1

1113888 1113889

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

N10

N20

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

100

100⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

(6)








δ12 lt 0 δ21 0 orδ12 0 δ21 lt 0







α1 = 002 α2 = 001δ12 = 00 δ21 = 00


10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 7





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity





α1 = 002 α2 = 001δ12 = 01 δ21 = 02

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

Popu

latio

n siz

e


Iteration times100 200 300 400 500 600 700 800 900 10000

α1 = 002 α2 = 001δ12 = 02 δ21 = ndash01

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e




α1 = 002 α2 = 001δ12 = 00 δ21 = ndash01

100 200 300 400 500 600 700 800 900 10000Iteration times

10

20

30

40

50

60

70

80

90

100

110

Popu

latio

n siz

e


8 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity







α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash02

0

20

40

60

80

100

120

140

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times



α1 = 002 α2 = 001δ12 = ndash01 δ21 = ndash01

0

20

40

60

80

100

120

Popu

latio

n siz

e

100 200 300 400 500 600 700 800 900 10000Iteration times


Complexity 9



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity



5 Conclusions





Data Availability




Acknowledgments


References











10 Complexity



































Complexity 11














12 Complexity



































Complexity 11














12 Complexity














12 Complexity

Documents

Symbiosis Evolution of Science Communication Ecosystem