Adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching

In this paper, the problem of the adaptive almost surely asymptotically synchronization for stochastic delayed neural networks with Markovian switching is considered. By utilizing a new nonnegative function and the M-matrix approach, we derive a sufficient condition to ensure adaptive almost surely asymptotically synchronization for stochastic delayed neural networks. Some appropriate parameters analysis and update laws are found via the adaptive feedback control techniques. We also present an illustrative numerical example to demonstrate the effectiveness of the M-matrix-based synchronization condition derived in this paper.

[1]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[2]  Yuhua Xu,et al.  Topology identification of the modified complex dynamical network with non-delayed and delayed coupling , 2012 .

[3]  E. Abed,et al.  Lyapunov and LMI analysis and feedback control of border collision bifurcations , 2007 .

[4]  Shengyuan Xu,et al.  Synchronization of stochastic chaotic neural networks with reaction-diffusion terms , 2012 .

[5]  Bing Li,et al.  Mean square function synchronization of chaotic systems with stochastic effects , 2012 .

[6]  Wenbing Zhang,et al.  Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances. , 2011, Chaos.

[7]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[8]  Chunmei Duan,et al.  Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity , 2009, Neurocomputing.

[9]  Jian-an Fang,et al.  Studying on the stability of fractional-order nonlinear system , 2012 .

[10]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[11]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

[12]  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.

[13]  B. Øksendal Stochastic differential equations : an introduction with applications , 1987 .

[14]  Jian-an Fang,et al.  Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling , 2009 .

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

[16]  Daniel W. C. Ho,et al.  Robust stability of stochastic delayed additive neural networks with Markovian switching , 2007, Neural Networks.

[17]  Jinde Cao,et al.  Adaptive synchronization for delayed neural networks with stochastic perturbation , 2008, J. Frankl. Inst..

[18]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[19]  Jinde Cao,et al.  Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation , 2009 .

[20]  H. Lutcke,et al.  Two-photon imaging and analysis of neural network dynamics , 2011, 1102.5528.

[21]  Guanrong Chen,et al.  Classification of Chaos in 3-d Autonomous Quadratic Systems-I: Basic Framework and Methods , 2006, Int. J. Bifurc. Chaos.

[22]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[23]  Yang Tang,et al.  Synchronization of Stochastic Delayed Neural Networks with Markovian Switching and its Application , 2009, Int. J. Neural Syst..

[24]  Selcuk Sevgen,et al.  Implementation of on-chip training system for cellular neural networks using iterative annealing optimisation method , 2010, Int. J. Reason. based Intell. Syst..

[25]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[26]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[27]  Yang Tang,et al.  Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays , 2011, Appl. Math. Comput..

[28]  Yonghui Sun,et al.  Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation , 2007 .

[29]  Wai Keung Wong,et al.  Impulsive pinning synchronization of stochastic discrete-time networks , 2010, Neurocomputing.