Limit cycles via higher order perturbations for some piecewise differential systems

dc.contributor.authorBuzzi, Claudio A. [UNESP]
dc.contributor.authorSilva Lima, Mauricio Firmino
dc.contributor.authorTorregrosa, Joan
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Federal do ABC (UFABC)
dc.contributor.institutionUniv Autonoma Barcelona
dc.date.accessioned2018-11-26T17:49:14Z
dc.date.available2018-11-26T17:49:14Z
dc.date.issued2018-05-15
dc.description.abstractA classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x', y') = (-y + epsilon f(x, y, epsilon), x + epsilon g(x, y, epsilon)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n, no more than Nn-1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Lienard differential systems providing better upper bounds for higher order perturbation in 8, showing also when they are reached. The Poincare-Pontryagin-Melnikov theory is the main technique used to prove all the results. (C) 2018 Elsevier B.V. All rights reserved.en
dc.description.affiliationUniv Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto, Brazil
dc.description.affiliationUniv Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210170 Santo Andre, SP, Brazil
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat, Sao Jose Do Rio Preto, Brazil
dc.description.sponsorshipMINECO
dc.description.sponsorshipAGAUR grant
dc.description.sponsorshipEuropean Community grants
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdMINECO: MTM2013-40998-P
dc.description.sponsorshipIdMINECO: MTM2016-77278-P
dc.description.sponsorshipIdAGAUR grant: 2014 SGR568
dc.description.sponsorshipIdEuropean Community grants: FP7-PEOPLE-2012-IRSES 316338
dc.description.sponsorshipIdEuropean Community grants: 318999
dc.description.sponsorshipIdFAPESP: 2012/18780-0
dc.description.sponsorshipIdFAPESP: 2013/24541-0
dc.description.sponsorshipIdFAPESP: 2017/03352-6
dc.format.extent28-47
dc.identifierhttp://dx.doi.org/10.1016/j.physd.2018.01.007
dc.identifier.citationPhysica D-nonlinear Phenomena. Amsterdam: Elsevier Science Bv, v. 371, p. 28-47, 2018.
dc.identifier.doi10.1016/j.physd.2018.01.007
dc.identifier.fileWOS000430766000003.pdf
dc.identifier.issn0167-2789
dc.identifier.lattes6682867760717445
dc.identifier.orcid0000-0003-2037-8417
dc.identifier.urihttp://hdl.handle.net/11449/164133
dc.identifier.wosWOS:000430766000003
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofPhysica D-nonlinear Phenomena
dc.relation.ispartofsjr0,861
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.subjectNon-smooth differential system
dc.subjectLimit cycle in Melnikov higher order perturbation
dc.subjectLienard piecewise differential system
dc.titleLimit cycles via higher order perturbations for some piecewise differential systemsen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.lattes6682867760717445[1]
unesp.author.orcid0000-0002-2753-1827[3]
unesp.author.orcid0000-0003-2037-8417[1]

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