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Journal of Applied Mathematics
Volume 2012, Article ID 693163, 12 pages
http://dx.doi.org/10.1155/2012/693163
Research Article

Exponential Stability for a Class of Stochastic Reaction-Diffusion Hopfield Neural Networks with Delays

1College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
2Department of Mathematics, Ocean University of China, Qingdao 266100, China

Received 7 August 2011; Accepted 28 November 2011

Academic Editor: Jitao Sun

Copyright © 2012 Xiao Liang and Linshan Wang. 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

This paper studies the asymptotic behavior for a class of delayed reaction-diffusion Hopfield neural networks driven by finite-dimensional Wiener processes. Some new sufficient conditions are established to guarantee the mean square exponential stability of this system by using Poincaré’s inequality and stochastic analysis technique. The proof of the almost surely exponential stability for this system is carried out by using the Burkholder-Davis-Gundy inequality, the Chebyshev inequality and the Borel-Cantelli lemma. Finally, an example is given to illustrate the effectiveness of the proposed approach, and the simulation is also given by using the Matlab.