Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 235038, 20 pages
doi:10.1155/2009/235038
Research Article

Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation

Xiaoqian Cui1 and Junjie Wei1,2

1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
2Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong 264209, China

Received 22 December 2008; Accepted 18 February 2009

Academic Editor: Binggen Zhang

Copyright © 2009 Xiaoqian Cui and Junjie Wei. 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

A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.