Advances in Difference Equations
Volume 2009 (2009), Article ID 410823, 18 pages
doi:10.1155/2009/410823
Research Article

Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

Jie Pan1,2 and Shouming Zhong1

1College of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
2Department of Mathematics, Sichuan Agricultural University, Yaan, Sichuan 625014, China

Received 13 June 2009; Revised 20 August 2009; Accepted 2 September 2009

Academic Editor: Tocka Diagana

Copyright © 2009 Jie Pan and Shouming Zhong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincaré inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions, which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results.