Mixed outer synchronization of coupled complex networks with time-varying coupling delay.

In this paper, the problem of outer synchronization between two complex networks with the same topological structure and time-varying coupling delay is investigated. In particular, we introduce a new type of outer synchronization behavior, i.e., mixed outer synchronization (MOS), in which different state variables of the corresponding nodes can evolve into complete synchronization, antisynchronization, and even amplitude death simultaneously for an appropriate choice of the scaling matrix. A novel nonfragile linear state feedback controller is designed to realize the MOS between two networks and proved analytically by using Lyapunov-Krasovskii stability theory. Finally, numerical simulations are provided to demonstrate the feasibility and efficacy of our proposed control approach.

[1]  G. Rangarajan,et al.  General stability analysis of synchronized dynamics in coupled systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Liisa Holm,et al.  Open Access Research Article Inferring the Physical Connectivity of Complex Networks from Their Functional Dynamics , 2022 .

[3]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

[4]  A. Winfree.  The geometry of biological time , 1991 .

[5]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[6]  Cristina Masoller,et al.  Synchronization in an array of globally coupled maps with delayed interactions , 2003 .

[7]  FU Xin-Chu,et al.  Topology Identification of General Dynamical Network with Distributed Time Delays , 2009 .

[8]  Cristina Masoller,et al.  Synchronization of globally coupled non-identical maps with inhomogeneous delayed interactions , 2004 .

[9]  L F Lago-Fernández,et al.  Fast response and temporal coherent oscillations in small-world networks. , 1999, Physical review letters.

[10]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[11]  Chai Wah Wu,et al.  Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  Xiaoping Xue,et al.  Outer synchronization of coupled networks using arbitrary coupling strength. , 2010, Chaos.

[13]  Xian Liu,et al.  Attractors of Fourth-Order Chua's Circuit and Chaos Control , 2007, Int. J. Bifurc. Chaos.

[14]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[15]  G. Zhong.  Implementation of Chua's circuit with a cubic nonlinearity , 1994 .

[16]  K. Thamilmaran,et al.  Hyperchaos in a Modified Canonical Chua's Circuit , 2004, Int. J. Bifurc. Chaos.

[17]  C. Wu,et al.  Chua's Equation with Cubic Nonlinearity , 1996 .

[18]  L. Chua,et al.  Canonical realization of Chua's circuit family , 1990 .

[19]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[20]  L. Chua,et al.  A universal circuit for studying and generating chaos. I. Routes to chaos , 1993 .

[21]  L. Chua,et al.  The double scroll family , 1986 .

[22]  Jinde Cao,et al.  Outer synchronization between two nonidentical networks with circumstance noise , 2010 .

[23]  Ying-Cheng Lai,et al.  Synchronization in complex networks with a modular structure. , 2006, Chaos.

[24]  T. Carroll,et al.  VOLUME-PRESERVING AND VOLUME-EXPANDING SYNCHRONIZED CHAOTIC SYSTEMS , 1997 .

[25]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[26]  Liang Chen,et al.  Adaptive synchronization between two complex networks with nonidentical topological structures , 2008 .

[27]  Michael Menzinger,et al.  Clustering and the synchronization of oscillator networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  W. Zheng,et al.  Generalized outer synchronization between complex dynamical networks. , 2009, Chaos.

[29]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[30]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[31]  Zhong-Ping Jiang,et al.  Topology identification of complex dynamical networks. , 2010, Chaos.

[32]  Jürgen Kurths,et al.  Synchronization between two coupled complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  P. K. Roy,et al.  Design of coupling for synchronization of chaotic oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Tianshou Zhou,et al.  Neurotransmitter-Mediated Collective Rhythms in Grouped Drosophila Circadian Clocks , 2008 .

[35]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[36]  Paulo C. Rech,et al.  Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity. , 2010, Chaos.

[37]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[38]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[39]  P. Hardin,et al.  Circadian rhythms from multiple oscillators: lessons from diverse organisms , 2005, Nature Reviews Genetics.

[40]  Lixin Tian,et al.  Linear generalized synchronization between two complex networks , 2010 .

[41]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[42]  S. K. Dana,et al.  Antisynchronization of Two Complex Dynamical Networks , 2009, Complex.

[43]  Zhong Chen,et al.  An intriguing hybrid synchronization phenomenon of two coupled complex networks , 2010, Appl. Math. Comput..

[44]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[45]  J. Kurths,et al.  Outer synchronization of coupled discrete-time networks. , 2009, Chaos.

[46]  Junan Lu,et al.  Structure identification of uncertain general complex dynamical networks with time delay , 2009, Autom..

[47]  Dirk Helbing,et al.  Decentralised control of material or traffic flows in networks using phase-synchronisation , 2006, physics/0603259.

[48]  E Oh,et al.  Modular synchronization in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.