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...
Saved in:
Published in | Discrete dynamics in nature and society Vol. 2013; pp. 1 - 9 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
Wiley
2013
|
Online Access | Get full text |
Cover
Loading…
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 |