Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones

Jaume Llibre; Douglas D. Novaes; Camila A. B. Rodrigues

doi:10.1016/j.physd.2017.05.003

paper

Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones

arXiv:1607.04086 · doi:10.1016/j.physd.2017.05.003

Abstract

This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z (x, y; ε)$ with many zones. We show that for $ε$ sufficiently small the averaged functions at any order control the existence of crossing limit cycles for systems in this family. We also provide some examples dealing with nonlinear centers.