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Volume 2017, Article ID 6292597, 9 pages
Research Article

Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

1Department of Mathematics, Chengdu Normal University, Chengdu 61130, China
2College of Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Ruofeng Rao; moc.361@oargnefour

Received 14 July 2017; Accepted 22 August 2017; Published 25 September 2017

Academic Editor: Chenguang Yang

Copyright © 2017 Ruofeng Rao 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.


This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.