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

Abstract

This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z(x,y;\epsilon)$ with many zones. We show that for $\epsilon$ 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.