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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 832892, 11 pages
http://dx.doi.org/10.1155/2014/832892
Research Article

Global Asymptotic Stability of Impulsive CNNs with Proportional Delays and Partially Lipschitz Activation Functions

1Department of Mathematics and Information Science, Chang’an University, Xi’an 710064, China
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Received 15 April 2014; Accepted 26 June 2014; Published 23 July 2014

Academic Editor: Ademir F. Pazoto

Copyright © 2014 Xueli Song and Jigen Peng. 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 researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation , the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.