Stability analysis for stochastic neural network with infinite delay

Authors:
Huan Su;Wenxue Li;Ke Wang;Xiaohua Ding
Affiliations:
Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China;Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China;Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China;Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China
Venue:
Neurocomputing
Year:
2011

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Abstract

This paper considers a stochastic neural network (SNN) with infinite delay. Some sufficient conditions for stochastic stability, stochastic asymptotical stability and global stochastic asymptotical stability, respectively, are derived by means of Lyapunov method, Ito formula and some inequalities. As a corollary, we show that if the neural network with infinite delay is stable under some conditions, then the stochastic stability is maintained provided the environmental noises are small. Estimates on the allowable sizes of environmental noises are also given. Finally, a three-dimensional SNN with infinite delay is analyzed and some numerical simulations are illustrated to show our results.