Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/84260 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |