Abstract and Applied Analysis
Volume 2013 (2013), Article ID 384981, 8 pages
http://dx.doi.org/10.1155/2013/384981
Research Article

Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays

Li Wan,1 Qinghua Zhou,2 Zhigang Zhou,1 and Pei Wang3

1School of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China
2Department of Mathematics, Zhaoqing University, Zhaoqing 526061, China
3School of Mathematics and Information Sciences, Henan University, Kaifeng 475004, China

Received 24 December 2012; Accepted 8 February 2013

Academic Editor: Kelin Li

Copyright © 2013 Li Wan et al. 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 investigates dynamical behaviors of the stochastic Hopfield neural networks with mixed time delays. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.