Abstract and Applied Analysis
Volume 2012 (2012), Article ID 909385, 11 pages
http://dx.doi.org/10.1155/2012/909385
Research Article

Bifurcation of a Cohen-Grossberg Neural Network with Discrete Delays

Qiming Liu1 and Wang Zheng2

1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2Department of Orthopaedics, Hebei Provincial People's Hospital, Shijiazhuang 050051, China

Received 7 January 2012; Accepted 31 January 2012

Academic Editor: Wing-Sum Cheung

Copyright © 2012 Qiming Liu and Wang Zheng. 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 simple Cohen-Grossberg neural network with discrete delays is investigated in this paper. The existence of local Hopf bifurcations is first considered by choosing the appropriate bifurcation parameter, and then explicit formulas are given to determine the direction of Hopf bifurcation and stability of the periodic solutions. Moreover, a set of sufficient conditions are given to guarantee the global Hopf bifurcation. Numerical simulations are given to illustrate the obtained results.