Stability of bidirectional associative memory neural networks with Markov switching via ergodic method and the law of large numbers

This paper devotes to stability analysis of continuous time and discrete time bidirectional associative memory (BAM) neural networks whose parameters are randomly varying in a finite state Markov chain sense. Based on the ergodic theory of continuous time Markov chain, the matrix measure approach and Lyapunov theory, almost sure stability and exponential stability in the mean square for continuous time BAM neural networks are derived. We also present some new stability results for discrete time BAM neural networks with the help of the law of large numbers. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in stability of neural networks.

[1]  Daoyi Xu,et al.  Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays , 2002, Int. J. Syst. Sci..

[2]  Jinde Cao,et al.  Exponential synchronization of chaotic neural networks: a matrix measure approach , 2009 .

[3]  Jinde Cao,et al.  Robust stability for uncertain stochastic neural network with delay and impulses , 2012, Neurocomputing.

[4]  S. Mohamad Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

[5]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[6]  Yuguang Fang,et al.  Stabilization of continuous-time jump linear systems , 2002, IEEE Trans. Autom. Control..

[7]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[8]  Xuerong Mao,et al.  RAZUMIKHIN-TYPE THEOREMS ON STABILITY OF STOCHASTIC NEURAL NETWORKS WITH DELAYS , 2001 .

[9]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[10]  Yuguang Fang Stability analysis of linear control systems with uncertain parameters , 1994 .

[11]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[12]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

[13]  Yuguang Fang,et al.  A new general sufficient condition for almost sure stability of jump linear systems , 1997, IEEE Trans. Autom. Control..

[14]  H. Kushner Stochastic Stability and Control , 2012 .

[15]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[16]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[17]  Réjean Plamondon,et al.  Stability analysis of bidirectional associative memory networks with time delays , 2003, IEEE Trans. Neural Networks.

[18]  Jinde Cao,et al.  Global asymptotic stability of bi-directional associative memory networks with distributed delays , 2004, Appl. Math. Comput..

[19]  Wenlian Lu,et al.  Global almost sure self-synchronization of Hopfield neural networks with randomly switching connections , 2011, Neural Networks.

[20]  Jinde Cao,et al.  Exponential stability analysis of uncertain stochastic neural networks with multiple delays , 2007 .

[21]  Jinde Cao,et al.  Lag Quasi-Synchronization of Coupled Delayed Systems With Parameter Mismatch , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[23]  W. J. Anderson Continuous-Time Markov Chains , 1991 .