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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 367589, 9 pages
http://dx.doi.org/10.1155/2013/367589
Research Article

Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received 2 February 2013; Accepted 5 April 2013

Academic Editor: Chunrui Zhang

Copyright © 2013 Ming Liu and Xiaofeng Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.