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EditorialAdvanced Topics in Modeling, Bifurcation Analysis, andControl Theory of Complex Systems
Olfa Boubaker ,1 Sajad Jafari ,2 Christos Volos ,3 Zeraoulia Elhadj,4
Viet-Thanh Pham ,5 and Jinde Cao 6
1National Institute of Applied Sciences and Technology, Tunis, Tunisia2Amirkabir University of Technology, Tehran, Iran3University of Thessaloniki, Thessaloniki, Greece4University of Tebessa, Tebessa, Algeria5Hanoi University of Science and Technology, Hanoi, Vietnam6Southeast University, Nanjing, China
Correspondence should be addressed to Olfa Boubaker; [email protected]
Received 22 November 2017; Accepted 23 November 2017; Published 26 February 2018
Copyright © 2018 Olfa Boubaker et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In the recent years, several complex systems have beeninvestigated in nonlinear theory and have had a huge impacton the scientist researches. Due to the complexity of theirdesign, analysis, and control, innovative insights had emergedin this expanding area.
The purpose of this special issue is to draw attentionof the scientific community to recent advances in nonlinearsystems theory and their possible applications. The spe-cial issue includes several high-quality papers written byleading and emerging specialists in the field. It proposesan array of novel complex models belonging to the classof chaotic/hyperchaotic systems, fractional-order nonlinearsystems, game systems, and smart grid and multiagent sys-tems. Stability analyses and bifurcation investigations are alsoexposed for severalmodels. Advanced control techniques andnovel synchronization approaches are moreover suggested.We can quote, in that sense, applications not only related tothe technology such as electronics and circuit design, multi-media, networks, and robotics but also related to biomedicaland market domains.
More than 37 submissions from 21 countries (Alge-ria, Cameroon, China, Egypt, Ethiopia, Greece, Honduras,Hong Kong, Iran, Iraq, Lithuania, Mexico, Pakistan, Poland,Saudi Arabia, Spain, Qatar, Thailand, Tunisia, Turkey, USA,and Vietnam) have been received. Among the articles
collected, a large number of high-quality papers existed,which led to 18 published articles with an acceptance rateof 45% (higher than that of the journal). This contri-bution reflects the strong interest in the considered sub-ject.
Among the published papers in the special issue, threeresearch papers propose novel hyperchaotic/chaotic systemssupported by engineering applications and three other paperssolve innovative chaos synchronization problems. Threepapers propose bifurcation investigations of complex modelsrelated to biomedical applications and another three paperspresent bifurcation analysis and control of game models.Finally, there are twopapers focusing on control ofmultiagentsystems, two papers on control of robotic systems in presenceof uncertainties, and two papers on control of coupledoscillators by external forcing. A very short description ofthe addressed topics, in the order of themes cited below, ispresented as follows.
In “Dynamic Analysis and Circuit Design of a NovelHyperchaotic System with Fractional-Order Terms,” by A.Lassoued and O. Boubaker, a novel hyperchaotic systemwith fractional-order polynomials is designed. Its highlycomplex dynamics are investigated in terms of equilibriumpoints, Lyapunov spectrum, and attractor forms and a relatedelectronic circuit is designed.
HindawiComplexityVolume 2018, Article ID 9417479, 3 pageshttps://doi.org/10.1155/2018/9417479
2 Complexity
In “Multimedia Security Application of a Ten-TermChaotic System without Equilibrium,” by X. Wang et al., anew chaotic system without equilibrium is proposed. Thesystem is realized on an electronic card and applied inmultimedia security, such as image encryption and soundsteganography.
In “A New Nonlinear Chaotic Complex Model and ItsComplex Antilag Synchronization,” by E. E. Mahmoud andF. S. Abood, a new chaotic Lu model with complex factors iscovered and a novel antilag synchronization approach is alsoproposed.
In “Chaos Control in Fractional Order Smart Gridwith Adaptive Sliding Mode Control and Genetically Opti-mized PID Control and Its FPGA Implementation,” by A.Karthikeyan and K. Rajagopal, a specific smart grid systemand its nonlinear properties are investigated. The Lyapunovexponents prove the existence of chaos and bifurcation. Arelated fractional order model is then derived and its bifurca-tion analysis is also investigated. Two different control meth-ods are finally proposed to suppress the chaotic oscillations.
In “Centralized and Decentralized Data-Sampling Prin-ciples for Outer-Synchronization of Fractional-Order NeuralNetworks,” by J.-E. Zhang, new sufficient criteria for an outer-synchronization of a fractional-order neural networks arederived using centralized and decentralized data-samplingprinciples.
In “Master-Slave Synchronization of 4D HyperchaoticRabinovich Systems,” by K. Ding et al., some original master-slave synchronization criteria are derived for 4DhyperchaoticRabinovich systems and then extended for 3D chaotic Rabi-novich systems.
In “Mixed Stimulus-Induced Mode Selection in Neu-ral Activity Driven by High and Low Frequency Currentunder Electromagnetic Radiation,” by L. Lu et al., a newHindmarsh-Rose neuron model with different types of elec-trical stimulus impended with a high-low frequency currentis proposed and deeply analyzed with regard to the transmis-sion of several complex signals.
In “Computer Simulation of Noise Effects of the Neigh-borhood of Stimulus Threshold for a Mathematical Modelof Homeostatic Regulation of Sleep-Wake Cycles,” by W. Jinet al., noise effects on sleep-wake cycles’ neuronal math-ematical model determined by the hypocretin/orexin andthe local glutamate interneurons spatiotemporal behaviorsare analyzed. The conductance and the activation variableof the modulation function are also investigated based on acircadian input skewed in sine function.
In “Autaptic Modulation of Electrical Activity in a Net-work of Neuron-Coupled Astrocyte,” by S. Guo et al., asimple network is developed for the Hodgkin-Huxley neuroncoupled by astrocyte and the autapse and different modesof electrical activities and oscillating behaviors are deeplyanalyzed.
In “Study on Triopoly Dynamic Game Model Based onDifferent Demand Forecast Methods in theMarket,” by J. Maet al., a new model of Triopoly game considering inaccuratedemand in the market is proposed. Bifurcation dynamics,route to chaos, and basins of attraction are investigated.Finally, a feedback control method is suggested.
In “Complexity Dynamic Character Analysis of RetailersBased on the Share of Stochastic Demand and Service,” by J.Ma et al., a modified price and demand game model basedon the stochastic demand and the retailer’s service level isproposed. The bifurcation phenomena as well the chaoticcharacteristics are shown. Finally, the chaos control of thecomplex model is achieved.
In “Nonlinear Complex Dynamics of Carbon EmissionReduction Cournot Game with Bounded Rationality,” byL. Zhao, a novel Cournot duopoly game model of carbonemission reduction based on the hypothesis of participant’sbounded rationality is proposed. The dynamic adjustmentmechanism of emission reduction for enterprises is analyzed.It is shown that the system can demonstrate chaotic phe-nomenon. Finally, a delay feedback control is designed tocontrol the system’s complex dynamics.
In “A Novel Clustering Method Based on Quasi-Consensus Motions of Dynamical Multiagent Systems,” byN. Cai et al., a novel approach for clustering based onquasi-consensus of dynamical high-ordermultiagent systemsis suggested and a necessary and sufficient condition forchecking the achievement of group consensus is given.
In “Leader-Follower Fixed-Time Group Consensus Con-trol of Multiagent Systems under Directed Topology,” by Y.Shang and Y. Ye, the fixed-time group consensus problem isinvestigated for a leader-follower network of integrators withdirected topology. A nonlinear distributed control protocol,based on local information, is proposed such that the followeragents in each subgroup are able to track their correspondingleaders in a prescribed convergence time regardless of theinitial conditions.
In “Design of Robust Supertwisting Algorithm BasedSecond-Order Sliding Mode Controller for Nonlinear Sys-temswith BothMatched andUnmatchedUncertainty,” byM.Jouini et al., amodified design of the super-twisting controllerfor nonlinear systems with matched and unmatched uncer-tainties is proposed.The main contribution resides in addingtwo terms to the classical design which leads to acceleratingthe convergence and simultaneously limiting the overshootand shortening the settling time of the system response.
In “Tracking Control for Mobile Robots Considering theDynamics of AllTheir Subsystems: Experimental Implemen-tation,” by J. R. Garcıa-Sanchez et al., the trajectory trackingtask in a wheeled mobile robot is solved by proposing athree-level hierarchical controller that considers the math-ematical model of the mechanical structure, actuators, andpower stage. Experimental results show the effectiveness androbustness of the proposed control scheme.
In “Multistability Analysis and Function Projective Syn-chronization in Relay Coupled Oscillators,” by A. T. Azaret al., regions of stability are discovered in a general classof Genesio−Tesi chaotic oscillators for which attractorsand limit cycles are shown and isospike diagrams are alsoexposed. Finally, finite-time projective synchronization ofrelay coupled oscillators is displayed.
In “Stabilization of a Network of the FitzHugh–NagumoOscillators by Means of a Single Capacitor Based RC FilterFeedback Technique,” by E. Adomaitiene et al., an originalcontrol approach for unstable FitzHugh–Nagumo oscillators
Complexity 3
is proposed based on analytical, numerical, and also exper-imental investigations. It is shown that a single capacitor issufficient to achieve this task if the oscillators are coupledstrongly enough.
Acknowledgments
The editors would like to express their thanks to all authorsof the special issue for their valuable contributions and to allreviewers for their useful efforts to provide valuable reviews.We expect this special issue to offer a timely view of advancedtopics in nonlinear systems, which will grant stimulation forfurther novel academic researches and innovative applica-tions.
Olfa BoubakerSajad Jafari
Christos VolosZeraoulia ElhadjViet-Thanh Pham
Jinde Cao
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