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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 385419, 9 pages
http://dx.doi.org/10.1155/2013/385419
Research Article

Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones

Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 1 March 2013; Accepted 16 April 2013

Academic Editor: Qingdu Li

Copyright © 2013 Yanyan Cheng. 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 study the bifurcation of limit cycles from periodic orbits of a four-dimensional system when the perturbation is piecewise linear with two switching boundaries. Our main result shows that when the parameter is sufficiently small at most, six limit cycles can bifurcate from periodic orbits in a class of asymmetric piecewise linear perturbed systems, and, at most, three limit cycles can bifurcate from periodic orbits in another class of asymmetric piecewise linear perturbed systems. Moreover, there are perturbed systems having six limit cycles. The main technique is the averaging method.