Abstract and Applied Analysis
Volume 2013 (2013), Article ID 167065, 10 pages
http://dx.doi.org/10.1155/2013/167065
Research Article

Delayed Feedback Control and Bifurcation Analysis of an Autonomy System

Zhen Wang,1 Huitao Zhao,2,3 and Xiangyu Kong1

1Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, China
2Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China
3Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China

Received 28 February 2013; Accepted 26 March 2013

Academic Editor: Yisheng Song

Copyright © 2013 Zhen Wang et al. 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

An autonomy system with time-delayed feedback is studied by using the theory of functional differential equation and Hassard’s method; the conditions on which zero equilibrium exists and Hopf bifurcation occurs are given, the qualities of the Hopf bifurcation are also studied. Finally, several numerical simulations are given; which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit.