Abstract and Applied Analysis
Volume 2012 (2012), Article ID 690453, 27 pages
http://dx.doi.org/10.1155/2012/690453
Research Article

Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems

Yanqin Xiong and Maoan Han

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 26 April 2012; Accepted 8 August 2012

Academic Editor: Alberto D'Onofrio

Copyright © 2012 Yanqin Xiong and Maoan Han. 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

We consider a class of discontinuous Liénard systems and study the number of limit cycles bifurcated from the origin when parameters vary. We establish a method of studying cyclicity of the system at the origin. As an application, we discuss some discontinuous Liénard systems of special form and study the cyclicity near the origin.