Exponential stability for stochastic reaction–diffusion BAM neural networks with time‐varying and distributed delays

Exponential stability for stochastic reaction–diffusion BAM neural networks with time‐varying and distributed delays

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Article ID: iaor20112847
Volume: 217
Issue: 13
Start Page Number: 6078
End Page Number: 6091
Publication Date: Mar 2011
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: stochastic processes
Abstract:

In this paper we study the stability for a class of stochastic bidirectional associative memory (BAM) neural networks with reaction–diffusion and mixed delays. The mixed delays considered in this paper are time‐varying and distributed delays. Based on a new Lyapunov–Krasovskii functional and the Poincaré inequality as well as stochastic analysis theory, a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution. The obtained results show that the reaction–diffusion term does contribute to the exponentially stabilization of the considered system. Moreover, two numerical examples are given to show the effectiveness of the theoretical results.

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