Discrete Dynamics in Nature and Society 
Volume 2006 (2006), Article ID 57254, 18 pages
doi:10.1155/DDNS/2006/57254

Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

Xiang-Ping Yan1,2 and Wan-Tong Li1

 1School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2School of Mathematics, Physics, and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
Received 8 September 2005; Accepted 5 December 2005

Abstract

We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.