Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

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dc.contributor.authorLlibre, Jaume
dc.contributor.authorda Silva, Paulo R. [UNESP]
dc.contributor.authorTeixeira, Marco A.
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T15:33:58Z
dc.date.available2014-05-20T15:33:58Z
dc.date.issued2009-01-01
dc.description.abstractIn this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.en
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
dc.description.affiliationIMECC UNICAMP, BR-13081970 São Paulo, Brazil
dc.description.affiliationIBILCE UNESP, Dept Matemat, BR-15054000 São Paulo, Brazil
dc.description.affiliationUnespIBILCE UNESP, Dept Matemat, BR-15054000 São Paulo, Brazil
dc.description.sponsorshipCICYT
dc.description.sponsorshipIdCICYT: 2005SGR 00550
dc.description.sponsorshipIdMTM2005-06098-C02-01
dc.format.extent508-526
dc.identifierhttp://dx.doi.org/10.1137/080722886
dc.identifier.citationSiam Journal on Applied Dynamical Systems. Philadelphia: Siam Publications, v. 8, n. 1, p. 508-526, 2009.
dc.identifier.doi10.1137/080722886
dc.identifier.fileWOS000265777800020.pdf
dc.identifier.issn1536-0040
dc.identifier.urihttp://hdl.handle.net/11449/42376
dc.identifier.wosWOS:000265777800020
dc.language.isoeng
dc.publisherSiam Publications
dc.relation.ispartofSiam Journal on Applied Dynamical Systems
dc.relation.ispartofjcr1.486
dc.relation.ispartofsjr1,040
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectRegularizationen
dc.subjectVector fieldsen
dc.subjectSingular perturbationen
dc.subjectDiscontinuous vector fieldsen
dc.subjectSliding vector fielden
dc.titleStudy of Singularities in Nonsmooth Dynamical Systems via Singular Perturbationen
dc.typeArtigo
dcterms.licensehttp://www.siam.org/journals/rcuk.php
dcterms.rightsHolderSiam Publications
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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Artigos - Matemática - IBILCE