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

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 cl...

Full description

Saved in:
Bibliographic Details
Published inDiscrete dynamics in nature and society Vol. 2013; pp. 1 - 9
Main Author Cheng, Yanyan
Format Journal Article
LanguageEnglish
Published Wiley 2013
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2013/385419