Relaxation oscillation in planar discontinuous piecewise smooth fast–slow systems

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorToniol Cardin, Pedro-
Data de aceite: dc.date.accessioned2025-08-21T23:21:39Z-
Data de disponibilização: dc.date.available2025-08-21T23:21:39Z-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2021-12-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1063/5.0048340-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/223274-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/223274-
Descrição: dc.descriptionThis paper provides a geometric analysis of relaxation oscillations in the context of planar fast–slow systems with a discontinuous right-hand side. We give conditions that guarantee the existence of a stable crossing limit cycle Γ ϵ when the singular perturbation parameter ϵ is positive and small enough. Moreover, in the singular limit ϵ → 0, the cycle Γ ϵ converges to a crossing closed singular trajectory. We also study the regularization of the crossing relaxation oscillator Γ ϵ and show that a (smooth) relaxation oscillation exists for the regularized vector field, which is a smooth fast–slow vector field with singular perturbation parameter ϵ. Our approach uses tools in geometric singular perturbation theory. We demonstrate the results to a number of examples including a model of an arch bridge with nonlinear viscous damping.-
Descrição: dc.descriptionDepartamento de Matemática Faculdade de Engenharia Universidade Estadual Paulista (UNESP)-
Descrição: dc.descriptionDepartamento de Matemática Faculdade de Engenharia Universidade Estadual Paulista (UNESP)-
Idioma: dc.languageen-
Relação: dc.relationChaos-
???dc.source???: dc.sourceScopus-
Título: dc.titleRelaxation oscillation in planar discontinuous piecewise smooth fast–slow systems-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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