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

24 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

Access to Document

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

https://ddd.uab.cat/record/182511

Cite this

@article{450b3082e10044efa86cd290afacb974,

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

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.",

keywords = "Averaging method, Nonsmooth differential system, Periodic solution, Piecewise smooth differential system",

author = "Jaume Llibre and Novaes, {Douglas D.} and Rodrigues, {Camila A.B.}",

year = "2017",

month = sep,

day = "1",

doi = "https://doi.org/10.1016/j.physd.2017.05.003",

language = "English",

volume = "353-354",

pages = "1--10",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

}

TY - JOUR

T1 - Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones

AU - Llibre, Jaume

AU - Novaes, Douglas D.

AU - Rodrigues, Camila A.B.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - © 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.

AB - © 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.

KW - Averaging method

KW - Nonsmooth differential system

KW - Periodic solution

KW - Piecewise smooth differential system

U2 - https://doi.org/10.1016/j.physd.2017.05.003

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

M3 - Article

VL - 353-354

SP - 1

EP - 10

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this