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dc.creatorCarmona Centeno, Victorianoes
dc.creatorFernández Sánchez, Fernandoes
dc.creatorNovaes, Douglas D.es
dc.date.accessioned2023-08-04T10:20:30Z
dc.date.available2023-08-04T10:20:30Z
dc.date.issued2023
dc.identifier.citationCarmona Centeno, V., Fernández Sánchez, F. y Novaes, D.D. (2023). Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region. Communications in Nonlinear Science and Numerical Simulation, 123, 107257. https://doi.org/10.1016/j.cnsns.2023.107257.
dc.identifier.issn1007-5704es
dc.identifier.urihttps://hdl.handle.net/11441/148406
dc.descriptionThis is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).es
dc.description.abstractIn this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line except for at most one point. In the research literature, many papers deal with the problem of determining the maximum number of limit cycles that these differential systems can have. This problem has been usually approached via large case-by-case analyses which distinguish the many different possibilities for the spectra of the matrices of the differential systems. Here, by using a novel integral characterization of Poincaré half-maps, we prove, without unnecessary distinctions of matrix spectra, that the optimal uniform upper bound for the number of limit cycles of these differential systems is one. In addition, it is proven that this limit cycle, if it exists, is hyperbolic and its stability is determined by a simple condition in terms of the parameters of the system. As a byproduct of our analysis, a condition for the existence of the limit cycle is also derived.es
dc.formatapplication/pdfes
dc.format.extent18 p.es
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofCommunications in Nonlinear Science and Numerical Simulation, 123, 107257.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectPiecewise planar linear differential systemses
dc.subjectSewing systemses
dc.subjectLimit cycleses
dc.subjectOptimal uniform upper boundes
dc.subjectPoincaré half-mapses
dc.subjectIntegral characterizationes
dc.titleUniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding regiones
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)es
dc.relation.projectIDPGC2018-096265-B-I00es
dc.relation.projectIDMTM2017-87915-C2-1-Pes
dc.relation.projectIDPID2021-123200NB-I00es
dc.relation.projectIDTIC-0130es
dc.relation.projectIDP12-FQM-1658es
dc.relation.projectIDUS-1380740es
dc.relation.projectIDP20-01160es
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S1007570423001752es
dc.identifier.doi10.1016/j.cnsns.2023.107257es
dc.contributor.groupUniversidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingenieríaes
dc.journaltitleCommunications in Nonlinear Science and Numerical Simulationes
dc.publication.volumen123es
dc.publication.initialPage107257es
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (MICINN). Españaes
dc.contributor.funderFondo Europeo de Desarrollo Regional (FEDER)es
dc.contributor.funderMinisterio de Economia, Industria y Competitividad (MINECO). Españaes
dc.contributor.funderConsejería de Educación y Ciencia. Junta de Andalucíaes
dc.contributor.funderConsejería de Economía, Conocimiento, Empresas y Universidad. Junta de Andalucíaes

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