Abstract and Applied Analysis
Volume 2012 (2012), Article ID 603535, 25 pages
http://dx.doi.org/10.1155/2012/603535
Research Article

Stochastic Synchronization of Reaction-Diffusion Neural Networks under General Impulsive Controller with Mixed Delays

Xinsong Yang,1 Chuangxia Huang,2 and Zhichun Yang1

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, China

Received 23 September 2012; Accepted 25 November 2012

Academic Editor: Sabri Arik

Copyright © 2012 Xinsong Yang 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 drive-response synchronization of a class of reaction-diffusion neural networks with time-varying discrete and distributed delays via general impulsive control method. Stochastic perturbations in the response system are also considered. The impulsive controller is assumed to be nonlinear and has multiple time-varying discrete and distributed delays. Compared with existing nondelayed impulsive controller, this general impulsive controller is more practical and essentially important since time delays are unavoidable in practical operation. Based on a novel impulsive differential inequality, the properties of random variables and Lyapunov functional method, sufficient conditions guaranteeing the global exponential synchronization in mean square are derived through strict mathematical proof. In our synchronization criteria, the distributed delays in both continuous equation and impulsive controller play important role. Finally, numerical simulations are given to show the effectiveness of the theoretical results.