editorial nonlinear analysis of dynamical complex...

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2013, Article ID 530124, 3 pageshttp://dx.doi.org/10.1155/2013/530124

EditorialNonlinear Analysis of Dynamical Complex Networks

Zidong Wang,1,2 Bo Shen,1 Hongli Dong,3,4 and Jun Hu4,5

1 School of Information Science and Technology, Donghua University, Shanghai 200051, China2Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK3College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China4Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China5 Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Correspondence should be addressed to Zidong Wang; [email protected]

Received 10 October 2013; Accepted 10 October 2013

Copyright © 2013 Zidong Wang 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.

Complex networks are composed of a large number of highlyinterconnected dynamical units and therefore exhibit verycomplicated dynamics. Examples of such complex networksinclude the Internet, that is, a network of routers or domains,theWorldWideWeb (WWW), that is, a network of websites,the brain, that is, a network of neurons, and an organization,that is, a network of people. Since the introduction of thesmall-world network principle, a great deal of research hasbeen focused on the dependence of the asymptotic behav-ior of interconnected oscillatory agents on the structuralproperties of complex networks. It has been found out thatthe general structure of the interaction network may play acrucial role in the emergence of synchronization phenomenain various fields such as physics, technology, and the lifesciences.

Complex networks have already become an ideal researcharea for control engineers, mathematicians, computer scien-tists, and biologists to manage, analyze, and interpret func-tional information from real-world networks. Sophisticatedcomputer system theories and computing algorithms havebeen exploited or emerged in the general area of computermathematics, such as analysis of algorithms, artificial intelli-gence, automata, computational complexity, computer secu-rity, concurrency and parallelism, data structures, knowledgediscovery, DNA and quantum computing, randomization,semantics, symbol manipulation, numerical analysis andmathematical software. This special issue aims to bringtogether the latest approaches to understanding complex net-works fromadynamic systemperspective. Topics include, but

are not limited to the following aspects of dynamics analysisfor complex networks: (a) synchronization and control, (b)topology structure and dynamics, (c) stability analysis, (d)robustness and fragility, and (e) Applications in real-worldcomplex networks.

We have solicited submissions to this special issue fromelectrical engineers, control engineers, mathematicians, andcomputer scientists. After a rigorous peer review process, 17papers have been selected that provide overviews, solutions,or early promises to manage, analyze, and interpret dynami-cal behaviors of complex systems. These papers have coveredboth the theoretical and practical aspects of complex systemsin the broad areas of dynamical systems, mathematics,statistics, operational research, and engineering.

This special issue starts with a survey paper on the recentadvances of multiobjective control and filtering problemsfor nonlinear stochastic systems with variance constraints.Specifically, in the paper entitled “Variance-constrained mul-tiobjective control and filtering for nonlinear stochastic systems:a survey” by L.Ma et al., the focus is to provide a timely reviewon the recent advances of the multiobjective control andfiltering issues for nonlinear stochastic systems with varianceconstraints. Firstly, the concepts of nonlinear stochastic sys-tems are recalled along with the introduction of some recentadvances. Then, the covariance control theory, which servesas a practicalmethod formultiobjective control design as wellas a foundation for linear system theory, is reviewed com-prehensively. The multiple design requirements frequentlyapplied in engineering practice for the use of evaluating

2 Abstract and Applied Analysis

system performances are introduced, including robustness,reliability and dissipativity. Several design techniques suit-able for the multiobjective variance-constrained control andfiltering problems for nonlinear stochastic systems are dis-cussed. The design objects (nonlinear stochastic system),design requirements (multiple performance specificationsincluding variance constraints), several design techniquesand a special case of the addressed problem, mixed 𝐻

2/𝐻∞

design problem, have been discussed in great detail withsome recent advances. Subsequently, some latest results onthe variance-constrained multiobjective control and filteringproblems for nonlinear stochastic systems are summarized.Finally, concluding remarks are drawn and several possiblefuture research directions are pointed out.

Complex networks have been extensively used in the-oretical analysis of dynamical complex systems, such asthe Internet, World Wide Web, communication networks,and social networks. Accordingly, the synchronization ofdynamics complex networks has attracted a great deal ofattention. In the paper entitled “Achieving synchronizationin arrays of coupled differential systems with time-varyingcouplings” by X. Yi et al., the synchronization problemis studied for complex dynamical networks described bylinearly coupled ordinary differential equation systems. Thetime-varying coupling is used to represent the interactionbetween individuals. A general sufficient condition is derivedsuch that the directed time-varying graph reaches consensus.Finally, a numerical simulation is provided to show theeffectiveness of the theoretical results. The synchronizationand reconstruction problem is investigated in “Chaos syn-chronization based on unknown input proportional multiple-integral fuzzy observer” by T. Youssef et al. for chaotic systems.An unknown input proportional multiple-integral observeris designed for synchronization of chaotic systems withimmeasurable decision variables and unknown input. Byusing the Lyapunov stability theory and the linear matrixinequality (LMI) technique, sufficient conditions are givento ensure the synchronization. In the work entitled “Syn-chronization of switched complex bipartite neural networkswith infinite distributed delays and derivative coupling” byQ. Bian et al., the synchronization problem is investigatedfor two coupled switched complex bipartite neural networks(SCBNNs) with distributed delays and derivative coupling.By constructing effective controllers, some synchronizationcriteria are proposed to ensure the synchronization of thesetwo SCBNNs. The distributed consensus problem is studiedin “Distributed impulsive consensus of the multiagent systemwithout velocity measurement” by Z. Liu et al. for continuous-time multiagent system under intermittent communication.An impulsive consensus algorithm is developed, where thelocal algorithm of each agent is only based on the positioninformation. Also, some necessary and sufficient conditionsfor consensus are given. Finally, a numerical example isgiven to illustrate the effectiveness of the theoretical analysis.Subsequently, in the paper entitled “Distributed consensus fordiscrete-time directed networks of multiagents with time-delaysand random communication links” by Y. Liu et al., the leader-following consensus problem is addressed for discrete-timedirected multiagent systems with time-delay and random

communication links. By constructing new Lyapunov func-tionals and employing some analytical techniques, sufficientconditions for the leader-following consensus in mean-square sense are established for multiagent system.

Over the past decades, the design of the controllers haslong been the mainstream of research topics and much efforthas been made for dynamical complex networks. In thepaper entitled “Sliding intermittent control for BAM neuralnetworks with delays” by J. Hu et al., the exponential stabilityproblem is firstly studied for a class of delayed bidirectionalassociative memory (BAM) neural networks with delays.By taking the advantages of the periodically intermittentcontrol idea and the impulsive control scheme, a slidingintermittent controller is designed for the addressed BAMsystem with time-delays. It is shown that such a slidingintermittent control method can comprise several kindsof control schemes as special cases. Also, some sufficientconditions are proposed such that the closed-loop delayedBAM neural networks are globally exponentially stable. Thedesign of nonfragile gain-scheduled controller is discussed in“Nonfragile gain-scheduled control for discrete-time stochasticsystems with randomly occurring sensor saturations” by W. Liet al. for a class of discrete stochastic systems with randomlyoccurring sensor saturations (ROSSs).The sensor saturationsoccur in a random way. By constructing the probability-dependent Lyapunov functional, a nonfragile gain-scheduledcontroller with the gain including both constant and time-varying parameters is designed such that the closed-loopsystem is exponentially stable in the mean-square sense.In the work entitled “Optimal guaranteed cost control ofa class of discrete-time nonlinear systems with Markovianswitching and mode-dependent mixed time-delays” by Y. Liu,the guaranteed cost control problem is addressed for a classof nonlinear discrete-time systems with Markovian jumpingparameters and mixed time-delays. The mixed time-delaysinclude both themode-dependent discrete delay and the infi-nite distributed delay with mode-dependent lower bound. Byconstructing novel Lyapunov-Krasovskii functionals, somesufficient conditions for the existence of guaranteed costcontrollers are derived. Also, a convex optimization approachis developed to minimize cost function so as to obtain theoptimal guaranteed cost controller. By using the dwell timeapproach, in the paper entitled “Stabilization and controllerdesign of 2D discrete switched systems with state delays underasynchronous switching” by S. Huang et al., the stabilityanalysis and controller design are conducted for 2D discreteswitched delayed systems represented by Roesser’s model.Accordingly, sufficient conditions are given such that theresulting closed-loop systems are exponentially stable.

In the past years, the stability analysis of the dynamicalcomplex networks has attracted much attention. In the workentitled “Ananalysis of stability of a class of neutral-type neuralnetworks with discrete time delays” by Z. Orman and S. Arik,the problems of existence, uniqueness, and global asymptoticstability are discussed for a class of neutral-type neuralnetwork with discrete time-delays. By employing a Lyapunovfunctional and using the homeomorphism mapping theo-rem, some new delay-independent sufficient conditions arederived to guarantee the existence, uniqueness, and global

Abstract and Applied Analysis 3

asymptotic stability of the equilibrium point. It is shown thatthe advantage of the proposed results is that the developedresults can be expressed in terms of network parametersonly. Finally, some examples are provided to compare theproposed results with the existing results and to illustratethe effectiveness of the main results. In the work entitled“Robust almost periodic dynamics for interval neural networkswith mixed time-varying delays and discontinuous activationfunctions” by H. Wu et al., the delay-dependent robustexponential stability problem is studied for almost periodicsolution of interval neural networks withmixed time-varyingdelays and discontinuous activation functions. According tothe nonsmooth Lyapunov stability theory and employing theLMI technique, a new delay-dependent criterion is givento guarantee the existence and globally exponential stabilityof almost periodic solution. Also, the proposed results areextended to prove the existence and robust stability of peri-odic solution for neural networks with mixed time-varyingdelays and discontinuous activations. Finally, a numericalexample is provided to show the feasibility of the devel-oped results.The problemof bounded-input bounded-output(BIBO) stability is investigated in “BIBO stability analysisfor delay switched systems with nonlinear perturbation” byJ. Wei et al. for a class of switched systems with mixedneutral delays and nonlinear perturbation. By constructingthe Lyapunov-Krasovskii functional, new BIBO stabilizationcriteria are derived. Finally, a numerical simulation is givento demonstrate the usefulness of the proposed results.

As is well known, the estimation theory has importantapplications in a variety of areas. In the work entitled“Deconvolution filtering for nonlinear stochastic systems withrandomly occurring sensor delays via probability-dependentmethod” by Y. Luo et al., the deconvolution filtering problemis studied for a class of discrete-time stochastic systems withrandomly occurring sensor delays and external stochasticnoises. By constructing the probability-dependent Lyapunovfunctional and employing convex optimization approach,sufficient condition is given to ensure the stability of theaddressed stochastic systems. The proposed gain-scheduledfilters include both constant parameters and time-varyinggains which can be updated online according to the measur-able missing probabilities in real time. It is shown that thedesired filters can be easily obtained by solving a set of linearmatrix inequalities (LMIs). Finally, a simulation exampleis provided to illustrate the feasibility and effectiveness ofthe proposed filtering scheme. Subsequently, in the paperentitled “Estimate of number of periodic solutions of second-order asymptotically linear difference system” by H. Bin andZ. Huang, the number of periodic solutions is discussed forsecond-order linear difference system. By using the Morsetheory and twist number, three cases are discussed. As thesystem is resonant at infinity, the perturbation method isused to study the compactness condition of functional. Somenew results are derived concerning the lower bounds ofthe nonconstant periodic solutions for discrete system. Inthe paper entitled “Convergence rate of numerical solutionsfor nonlinear stochastic pantograph equations with Marko-vian switching and jumps” by Z. W. Lu et al., the studyof convergence rate is addressed for nonlinear stochastic

pantograph equations withMarkovian switching and Poissonjump. Sufficient conditions of existence and uniqueness ofthe solutions are given for nonlinear stochastic pantographequations with Markovian switching and jumps. It is shownthat Euler-Maruyama scheme for nonlinear stochastic pan-tograph equations with Markovian switching and Brownianmotion is of convergence with strong order 1/2. The mean-square convergence is preferable to be used for nonlinearstochastic pantograph equations with Markovian switchingand pure jumps. Accordingly, the order of mean-squareconvergence is close to 1/2. Moreover, the impact of humandynamics on the information propagation in online socialnetworks is discussed in “Information propagation in onlinesocial network based on human dynamics” by Q. Yan etal. Also, an extended susceptible-infected (SI) propagationmodel is proposed to incorporate bursty human activitypatterns and limited attention. The proposed result can beused to optimize/control the information propagation inonline social networks.

Acknowledgments

This special issue is a timely reflection of the research progressin the area of nonlinear analysis of dynamical complexnetworks. We would like to acknowledge all authors for theirefforts in submitting high-quality papers. We are also verygrateful to the reviewers for their thorough and on-timereviews of the papers.

Zidong WangBo Shen

Hongli DongJun Hu

Submit your manuscripts athttp://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttp://www.hindawi.com

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com

Volume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Stochastic AnalysisInternational Journal of

editorial nonlinear analysis of dynamical complex...

Documents