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2013 Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation
Ming Liu, Xiaofeng Xu
Abstr. Appl. Anal. 2013(SI20): 1-9 (2013). DOI: 10.1155/2013/367589


The dynamics of a 2-dimensional neural network model in neutral form are investigated. We prove that a sequence of Hopf bifurcations occurs at the origin as the delay increases. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using normal form method and center manifold theory. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. Finally, some numerical simulations are carried out to support the analytic results.


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Ming Liu. Xiaofeng Xu. "Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation." Abstr. Appl. Anal. 2013 (SI20) 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1277.34105
MathSciNet: MR3049329
Digital Object Identifier: 10.1155/2013/367589

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI20 • 2013
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