Stability and bifurcation in a simplified four-neuron BAM neural network with  multiple delays

Yan, Xiang-Ping; Li, Wan-Tong

doi:https://doi.org/10.1155/DDNS/2006/32529

Discrete Dynamics in Nature and Society

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Volume 2006 | Article ID 032529 | https://doi.org/10.1155/DDNS/2006/32529

Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays

Xiang-Ping Yan^1,2and Wan-Tong Li²

Received23 May 2005

Accepted04 Sept 2005

Published22 Feb 2006

Abstract

We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM) neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. 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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