Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

Ren, Yaping; Li, Yongkun

doi:https://doi.org/10.1155/2007/84260

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 084260 | https://doi.org/10.1155/2007/84260

Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

Yaping Ren¹and Yongkun Li¹

Academic Editor: Virginia Kiryakova

Received21 Sept 2006

Revised18 Jan 2007

Accepted27 Feb 2007

Published26 Apr 2007

Abstract

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The direction and the stability of the Neimark-Sacker bifurcation are investigated by applying the normal form theory and the center manifold theorem.

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Copyright

Copyright © 2007 Yaping Ren and Yongkun 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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