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Mathematical Problems in Engineering
Volume 2017, Article ID 6987436, 22 pages
Research Article

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

1Institute of Applied Mathematics, Hebei Academy of Sciences, No. 46 South Youyi Street, Shijiazhuang 050081, China
2Hebei Authentication Technology Engineering Research Center, No. 46 South Youyi Street, Shijiazhuang 050081, China
3Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 West Heping Road, Shijiazhuang 050003, China

Correspondence should be addressed to Zhiqiang Wang; gro.htam-beh@gnaiqihzgnaw

Received 20 February 2017; Accepted 2 May 2017; Published 20 August 2017

Academic Editor: Marco Mussetta

Copyright © 2017 Zhiqiang Wang 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.


We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of -norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results.