Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay
We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method an...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/357382 |
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| Summary: | We consider the nonlinear dynamical behavior of a
three-dimensional recurrent neural network with time delay. By choosing the
time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs
when the delay passes through a sequence of critical values. Applying the nor-
mal form method and center manifold theory, we obtain some local bifurcation
results and derive formulas for determining the bifurcation direction and the
stability of the bifurcated periodic solution. Some numerical examples are also
presented to verify the theoretical analysis. |
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| ISSN: | 1110-757X 1687-0042 |