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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 917835, 11 pages
http://dx.doi.org/10.1155/2013/917835
Research Article

Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2Training Department, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 21 March 2013; Revised 22 May 2013; Accepted 22 May 2013

Academic Editor: Seenith Sivasundaram

Copyright © 2013 Yanke Du 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.

Abstract

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure that -dimensional Cohen-Grossberg neural networks with -level discontinuous activation functions can have equilibrium points or periodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.