Stochastic synchronization for complex dynamical networks with time-varying couplings

In this paper, the stochastic synchronization problem is investigated for complex dynamical networks with unknown periodic time-varying couplings and with stochastic noise perturbations. By using Lyapunov stability theory, inequality techniques, the properties of Weiner process and adding suitable controllers, sufficient conditions are obtained to ensure stochastic synchronization for complex dynamical networks. Adaptive periodic learning laws are designed for unknown time-varying coupling parameters. Theoretical analysis and numerical simulation fully verify the main results.

[1]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[2]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

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

[5]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[6]  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.

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

[8]  Maurizio Porfiri,et al.  Criteria for global pinning-controllability of complex networks , 2008, Autom..

[9]  Shiqun Zhu,et al.  Synchronization in complex networks by time-varying couplings , 2008 .

[10]  Wenlian Lu,et al.  Chaos synchronization in networks of coupled maps with time-varying topologies , 2008, 0812.2648.

[11]  Zhang Yi,et al.  Synchronization analysis of delayed complex networks with time-varying couplings , 2008 .

[12]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

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

[15]  Ya Zhang,et al.  Global synchronization of stochastic delayed complex networks , 2012, Nonlinear Dynamics.

[16]  Junmi Li,et al.  Adaptive Synchronization of Nonlinearly Parameterized Complex Dynamical Networks with Unknown Time-Varying Parameters , 2012 .

[17]  Guang-Hong Yang,et al.  Adaptive synchronization of a class of nonlinearly coupled complex networks , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[18]  Ju H. Park,et al.  Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling , 2012, Appl. Math. Comput..

[19]  Wai Keung Wong,et al.  Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays , 2012, J. Optim. Theory Appl..

[20]  Yi-Zheng Fan,et al.  Adaptive synchronization in complex dynamical networks with coupling delays for general graphs , 2012, Appl. Math. Comput..

[21]  Junmin Li,et al.  Stochastic adaptive synchronization for time-varying complex delayed dynamical networks with heterogeneous nodes , 2013, Appl. Math. Comput..

[22]  Impulsive generalized function synchronization of complex dynamical networks , 2013 .

[23]  Tianping Chen,et al.  Synchronization of networks with time-varying couplings , 2013 .

[24]  Hongfang Liu,et al.  Adaptive cluster synchronization for a complex dynamical network with delays and stochastic perturbation , 2013 .

[25]  Rong Li,et al.  Adaptive Synchronization of Complex Dynamical Networks with Time-Varying Delays , 2013, Circuits, Systems, and Signal Processing.

[26]  Xinsong Yang,et al.  Synchronization of TS fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects , 2014, Fuzzy Sets Syst..

[27]  Wenwu Yu,et al.  Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach , 2014, Neural Networks.

[28]  Wenbing Zhang,et al.  Finite-time cluster synchronisation of Markovian switching complex networks with stochastic perturbations , 2014 .

[29]  Lixiang Li,et al.  Stochastic synchronization of complex network via a novel adaptive nonlinear controller , 2014 .

[30]  Jinde Cao,et al.  Hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations , 2014, Appl. Math. Comput..