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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 109319, 14 pages
http://dx.doi.org/10.1155/2012/109319
Research Article

Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

1School of Mathematics and Physics, Anhui University of Technology, Ma'anshan 243002, China
2School of Computer Science, Anhui University of Technology, Ma'anshan 243002, China

Received 12 September 2012; Accepted 23 October 2012

Academic Editor: Sabri Arik

Copyright © 2012 Yanyan Wang and Jianping Zhou. 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

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of -matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.