Cluster mixed synchronization via pinning control and adaptive coupling strength in community networks with nonidentical nodes

Abstract In this paper, complex networks with community structure and nonidentical nodes are investigated. The cluster mixed synchronization of these networks is studied by using some linear pinning control schemes. Only the nodes in one community which have direct connections to the nodes in other communities are controlled. Adaptive coupling strength method is adopted to achieve the synchronization as well. According to Lyapunov stability theory, several sufficient conditions for the network to achieve cluster mixed synchronization are derived. Numerical simulations are provided to verify the correctness and the effectiveness of the theoretical results.

[1]  Michael Small,et al.  Generation of clusters in complex dynamical networks via pinning control , 2008 .

[2]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[3]  Xing-yuan Wang,et al.  Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control , 2009 .

[4]  Jürgen Kurths,et al.  Consensus over directed static networks with arbitrary finite communication delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Song Zheng,et al.  Impulsive synchronization of complex networks with non-delayed and delayed coupling , 2009 .

[6]  M. Porfiri,et al.  Node-to-node pinning control of complex networks. , 2009, Chaos.

[7]  Linying Xiang,et al.  On pinning synchronization of general coupled networks , 2011 .

[8]  Tianping Chen,et al.  Cluster synchronization in networks of coupled nonidentical dynamical systems. , 2009, Chaos.

[9]  Adrian P. Martin,et al.  Persistence of cluster synchronization under the influence of advection. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Xinchu Fu,et al.  Cluster synchronization in community networks with nonidentical nodes. , 2009, Chaos.

[11]  Ji Xiang,et al.  Analysis of Pinning-Controlled Networks: A Renormalization Approach , 2009, IEEE Transactions on Automatic Control.

[12]  Wang Jing,et al.  A Novel Adaptive Observer-Based Control Scheme for Synchronization and Suppression of a Class of Uncertain Chaotic Systems , 2009 .

[13]  Qinghua Ma,et al.  Mixed outer synchronization of coupled complex networks with time-varying coupling delay. , 2011, Chaos.

[14]  A. Khaki-Sedigh,et al.  Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement , 2009 .

[15]  Zhidong Teng,et al.  Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. , 2010, Chaos.

[16]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[17]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[18]  Yiguang Liu,et al.  Global synchronization for directed complex networks , 2010 .

[19]  Jari Saramäki,et al.  Emergence of communities in weighted complex networks , 2007 .

[20]  Francesca Fiorilli,et al.  Experiments on node-to-node pinning control of Chua’s circuits , 2010 .

[21]  Jari Saramäki,et al.  Emergence of communities in weighted networks. , 2007, Physical review letters.

[22]  Xiaomei Feng,et al.  Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects , 2011 .

[23]  Manfeng Hu,et al.  Projective cluster synchronization in drive-response dynamical networks , 2008 .

[24]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..