Periodic orbits for perturbations of piecewise linear systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Carmona, Victoriano¹  Fernandez-Garcia, Soledad¹  Freire, Emilio¹ 

[1] Univ Seville, Dept Matemat Aplicada 2, Escuela Super Ingn, Seville 41092, Spain

关键词: Piecewise linear systems;    Periodic orbits;    Invariant manifolds;    Melnikov function;    Averaging method;   

DOI  :  10.1016/j.jde.2010.10.025

来源: Elsevier

【 摘 要 】

We consider the existence of periodic orbits in a class of three-dimensional piecewise linear systems. Firstly, we describe the dynamical behavior of a non-generic piecewise linear system which has two equilibria and one two-dimensional invariant manifold foliated by periodic orbits. The aim of this work is to study the periodic orbits of the continuum that persist under a piecewise linear perturbation of the system. In order to analyze this situation, we build a real function of real variable whose zeros are related to the limit cycles that remain after the perturbation. By using this function, we state some results of existence and stability of limit cycles in the perturbed system, as well as results of bifurcations of limit cycles. The techniques presented are similar to the Melnikov theory for smooth systems and the method of averaging. (c) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free