Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays. (14th May 2006)

• Record Type: Journal Article
• Authors: Yan, Xiang-Ping; Li, Wan-Tong
• Is Part Of: Discrete dynamics in nature and society. Volume 2006(2006)
• Publication Date: 2006-05-14
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/DDNS/2006/57254
• Languages: English
• ISSNs: 1026-0226

Abstract

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.