Global exponential synchronization for coupled switched delayed recurrent neural networks with stochastic perturbation and impulsive effects

Abstract This paper focuses on the hybrid effects of stochastic perturbation, system switching, state delays and impulses on neural networks. Based on the Lyapunov functional method, switching analysis techniques, the comparison principle and a new impulsive delay differential inequality, we derive some sufficient conditions which depend on delay and impulses to guarantee the exponential synchronization of the coupling delay switching recurrent neural networks with stochastic perturbation. Simulation results finally demonstrate the effectiveness of the theoretical results.

[1]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Linlin Hou,et al.  Robust l2−l∞ state feedback control for uncertain discrete-time switched systems with mode-dependent time-varying delays† , 2010 .

[3]  Shaocheng Tong,et al.  Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach , 2014, Fuzzy Sets Syst..

[4]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[5]  Wenwu Yu,et al.  Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems , 2010, Autom..

[6]  A. Friedman.  Stochastic Differential Equations and Applications , 1975 .

[7]  Madan M. Gupta,et al.  Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory , 2003 .

[8]  Xiao Fan Wang,et al.  Complex Networks: Topology, Dynamics and Synchronization , 2002, Int. J. Bifurc. Chaos.

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

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

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

[12]  Chuandong Li,et al.  Bogdanov–Takens Singularity in Tri-Neuron Network With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Peng Shi,et al.  Sampled-Data Exponential Synchronization of Complex Dynamical Networks With Time-Varying Coupling Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[15]  Dong Yang,et al.  Robust finite-time H∞ control for Markovian jump systems with partially known transition probabilities , 2013, J. Frankl. Inst..

[16]  Ting Wang,et al.  Exponential synchronization for delayed chaotic neural networks with nonlinear hybrid coupling , 2012, Neurocomputing.

[17]  Tingwen Huang,et al.  Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Zhidong Teng,et al.  Adaptive synchronization in an array of linearly coupled neural networks with reaction–diffusion terms and time delays , 2012 .

[20]  Martin J. Gander,et al.  Corrections to Optimized Waveform Relaxation Methods for Longitudinal Partitioning of Transmission Lines [Aug 09 1732-1743] , 2010, IEEE Trans. Circuits Syst. I Regul. Pap..

[21]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Huaguang Zhang,et al.  Synchronization stability in complex interconnected neural networks with nonsymmetric coupling , 2013, Neurocomputing.

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

[24]  Lei Wang,et al.  Synchronization in complex networks with switching topology , 2011 .

[25]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

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

[28]  Yongcan Cao,et al.  Exponential l2−l∞ output tracking control for discrete‐time switched system with time‐varying delay , 2012 .

[29]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[30]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[31]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Jinde Cao,et al.  Synchronization of delayed complex dynamical networks with impulsive and stochastic effects , 2011 .

[33]  Wei Xing Zheng,et al.  Finite-time stabilization for a class of switched time-delay systems under asynchronous switching , 2013, Appl. Math. Comput..

[34]  J. Kurths,et al.  Identifying Controlling Nodes in Neuronal Networks in Different Scales , 2012, PloS one.

[35]  Qiankun Song,et al.  Synchronization of Chaotic Delayed Fuzzy Neural Networks under Impulsive and Stochastic Perturbations , 2013 .

[36]  Huijun Gao,et al.  A Constrained Evolutionary Computation Method for Detecting Controlling Regions of Cortical Networks , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[37]  Huaguang Zhang,et al.  Novel synchronization analysis for complex networks with hybrid coupling by handling multitude Kronecker product terms , 2012, Neurocomputing.

[38]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[39]  Linlin Hou,et al.  Robust l2−l∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched System with Mode-Dependent Time-Varying Delays , 2011, Circuits Syst. Signal Process..

[40]  Qiang Shen,et al.  Closed form fuzzy interpolation , 2013, Fuzzy Sets Syst..

[41]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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