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2013 Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays
Zizhen Zhang, Huizhong Yang
J. Appl. Math. 2013: 1-13 (2013). DOI: 10.1155/2013/436254

Abstract

A four-dimensional recurrent neural network with two delays is considered. The main result is given in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory. Some numerical examples are also presented to verify the theoretical analysis.

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Zizhen Zhang. Huizhong Yang. "Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays." J. Appl. Math. 2013 1 - 13, 2013. https://doi.org/10.1155/2013/436254

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950676
MathSciNet: MR3131005
Digital Object Identifier: 10.1155/2013/436254

Rights: Copyright © 2013 Hindawi

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