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Journal of Applied Mathematics
Volume 2013, Article ID 482351, 16 pages
http://dx.doi.org/10.1155/2013/482351
Research Article

Control of Hopf Bifurcation in Autonomous System Based on Washout Filter

Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China

Received 4 July 2013; Accepted 7 September 2013

Academic Editor: Erik Van Vleck

Copyright © 2013 Wenju Du 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

In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium . Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems.