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:https://doi.org/10.1016/j.physd.2017.05.003

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

14 Citations (Scopus)

Abstract

© 2017 Elsevier B.V. This work is devoted to study the existence of periodic solutions for a class of ε-family of discontinuous differential systems with many zones. We show that the averaged functions at any order control the existence of crossing limit cycles for systems in this class. We also provide some examples dealing with nonsmooth perturbations of nonlinear centers.

Original language	English
Pages (from-to)	1-10
Journal	Physica D: Nonlinear Phenomena
Volume	353-354
DOIs	https://doi.org/10.1016/j.physd.2017.05.003
Publication status	Published - 1 Sep 2017

Keywords

Averaging method
Nonsmooth differential system
Periodic solution
Piecewise smooth differential system

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abstract = "{\textcopyright} 2017 Elsevier B.V. This work is devoted to study the existence of periodic solutions for a class of ε-family of discontinuous differential systems with many zones. We show that the averaged functions at any order control the existence of crossing limit cycles for systems in this class. We also provide some examples dealing with nonsmooth perturbations of nonlinear centers.",

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KW - Averaging method

KW - Nonsmooth differential system

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KW - Piecewise smooth differential system

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