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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 131836, 10 pages
http://dx.doi.org/10.1155/2013/131836
Research Article

Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality

School of Economics & Management, Nanjing University of Information Science & Technology, Nanjing 210044, China

Received 15 November 2012; Accepted 8 February 2013

Academic Editor: Qi Luo

Copyright © 2013 Xianghong Lai and Tianxiang Yao. 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 work is devoted to the stability study of impulsive cellular neural networks with time-varying delays and reaction-diffusion terms. By means of new Poincaré integral inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some novel and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and show that not only the reaction-diffusion coefficients but also the regional features including the boundary and dimension of spatial variable can influence the stability. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.