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

Yan, Xiang-Ping; Li, Wan-Tong

doi:https://doi.org/10.1155/DDNS/2006/57254

Discrete Dynamics in Nature and Society

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Volume 2006 | Article ID 057254 | https://doi.org/10.1155/DDNS/2006/57254

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

Xiang-Ping Yan^1,2and Wan-Tong Li¹

Received08 Sept 2005

Accepted05 Dec 2005

Published14 May 2006

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.

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Copyright

Copyright © 2006 Xiang-Ping Yan and Wan-Tong Li. 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.

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