Abstract and Applied Analysis

Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation

Ming Liu and Xiaofeng Xu

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 367589, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449627

Digital Object Identifier
doi:10.1155/2013/367589

Mathematical Reviews number (MathSciNet)
MR3049329

Zentralblatt MATH identifier
1277.34105

Citation

Liu, Ming; Xu, Xiaofeng. Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 367589, 9 pages. doi:10.1155/2013/367589. https://projecteuclid.org/euclid.aaa/1393449627


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