Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control

In this paper, we focus on the problem of driving a general network to a selected cluster synchronization pattern by means of a pinning control strategy. Sufficient conditions are presented to guarantee the realization of the cluster synchronization pattern for all initial values. We also show the detailed steps on how to construct the coupling matrix and to modify the control strengths. Moreover, the method of adapting the coupling strength is provided to refine the result.

[1]  V. I. Krinsky,et al.  Image processing using light-sensitive chemical waves , 1989, Nature.

[2]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

[3]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[4]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[5]  M. Cross,et al.  Pinning control of spatiotemporal chaos , 1997, chao-dyn/9705001.

[6]  Roy,et al.  Communication with chaotic lasers , 1998, Science.

[7]  R. Femat,et al.  On the chaos synchronization phenomena , 1999 .

[8]  T. Glad,et al.  On Diffusion Driven Oscillations in Coupled Dynamical Systems , 1999 .

[9]  M. D. S. Vieira Chaos and Synchronized Chaos in an Earthquake Model , 1998, cond-mat/9811305.

[10]  Belykh,et al.  Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  V N Belykh,et al.  Cluster synchronization modes in an ensemble of coupled chaotic oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  L. Glass Synchronization and rhythmic processes in physiology , 2001, Nature.

[13]  H. Nijmeijer,et al.  Partial synchronization: from symmetry towards stability , 2002 .

[14]  M. Hasler,et al.  Persistent clusters in lattices of coupled nonidentical chaotic systems. , 2003, Chaos.

[15]  Martin Hasler,et al.  Cluster Synchronization in Three-Dimensional Lattices of Diffusively Coupled oscillators , 2003, Int. J. Bifurc. Chaos.

[16]  Guanrong Chen,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Charles M. Gray,et al.  Synchronous oscillations in neuronal systems: Mechanisms and functions , 1994, Journal of Computational Neuroscience.

[19]  Tianping Chen,et al.  Chaotic Lag Synchronization of Coupled Delayed Neural Networks and Its Applications in Secure Communication , 2005 .

[20]  M. Markus,et al.  Control of spatiotemporal chaos: dependence of the minimum pinning distance on the spatial measure entropy , 2005 .

[21]  Gang Zhang,et al.  A new method to realize cluster synchronization in connected chaotic networks. , 2006, Chaos.

[22]  Guo-Ping Jiang,et al.  A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Antonio Loría,et al.  Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Y. Lai,et al.  Optimization of synchronization in gradient clustered networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Z. Duan,et al.  Analyzing and controlling the network synchronization regions , 2007 .

[27]  Z. Duan,et al.  Complex network synchronizability: analysis and control. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  E. Ott,et al.  Network synchronization of groups. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Tianping Chen,et al.  Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling , 2007 .

[30]  Junan Lu Cluster Synchronization in a Complex Dynamical Network with Two Nonidentical Clusters , 2008, J. Syst. Sci. Complex..

[31]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[32]  Tianping Chen,et al.  Partial synchronization in linearly and symmetrically coupled ordinary differential systems , 2009 .