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

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

Dynamical Systems 2018-09-11 v1

Authors: Jaume Llibre , Douglas D. Novaes , Camila A. B. Rodrigues

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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.

Keywords

averaging theory limit cycles discontinuous piecewise systems periodic solutions nonlinear centers

Cite

@article{arxiv.1607.04086,
  title  = {Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones},
  author = {Jaume Llibre and Douglas D. Novaes and Camila A. B. Rodrigues},
  journal= {arXiv preprint arXiv:1607.04086},
  year   = {2018}
}

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