Persistence of periodic solutions from discontinuous planar piecewise linear Hamiltonian differential systems with three zones

dc.contributor.authorPessoa, Claudio [UNESP]
dc.contributor.authorRibeiro, Ronisio [UNESP]
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.date.accessioned2023-03-01T20:18:21Z
dc.date.available2023-03-01T20:18:21Z
dc.date.issued2022-01-01
dc.description.abstractIn this paper, we study the number of limit cycles that can bifurcate from a period annulus in discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. More precisely, we consider the case where the period annulus, bounded by a heteroclinic orbit or homoclinic loop, is obtained from a real center of the central subsystem, i.e. the system defined between the two parallel lines, and two real saddles of the others subsystems. Denoting by H(n) the number of limit cycles that can bifurcate from this period annulus by polynomial perturbations of degree n, we prove that if the period annulus is bounded by a heteroclinic orbit then H(1) ≥ 2 , H(2) ≥ 3 and H(3) ≥ 5. Now, if the period annulus is bounded by a homoclinic loop then H(1) ≥ 3 , H(2) ≥ 4 and H(3) ≥ 7. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system.en
dc.description.affiliationInstituto de Biociências Letras e Ciências Exatas) Universidade Estadual Paulista (UNESP, R. Cristovão Colombo, 2265, SP
dc.description.affiliationUnespInstituto de Biociências Letras e Ciências Exatas) Universidade Estadual Paulista (UNESP, R. Cristovão Colombo, 2265, SP
dc.identifierhttp://dx.doi.org/10.1007/s40863-022-00313-z
dc.identifier.citationSao Paulo Journal of Mathematical Sciences.
dc.identifier.doi10.1007/s40863-022-00313-z
dc.identifier.issn2316-9028
dc.identifier.issn1982-6907
dc.identifier.scopus2-s2.0-85134221858
dc.identifier.urihttp://hdl.handle.net/11449/240466
dc.language.isoeng
dc.relation.ispartofSao Paulo Journal of Mathematical Sciences
dc.sourceScopus
dc.subjectHamiltonian systems
dc.subjectLimit Cycles
dc.subjectPeriod annulus
dc.subjectPiecewise linear differential system
dc.titlePersistence of periodic solutions from discontinuous planar piecewise linear Hamiltonian differential systems with three zonesen
dc.typeArtigo
unesp.author.orcid0000-0001-6790-1055[1]

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