Slow–fast systems and sliding on codimension 2 switching manifolds

In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > 0 satisfying that X ε,η converges uniformly to X in each compact subset of R...

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Detalles Bibliográficos
Autores: da Silva, Paulo Ricardo [UNESP], Nunes, Willian Pereira [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/188805
Acceso en línea:http://dx.doi.org/10.1080/14689367.2019.1579782
http://hdl.handle.net/11449/188805
Access Level:acceso abierto
Palabra clave:Bogdanov–Takens bifurcation
Hopf bifurcation
invariant manifolds
non-smooth systems
Singular perturbation
Descripción
Sumario:In this work, we consider piecewise smooth vector fields X defined in R n \ ∑, where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields X ε.η , ε,η > 0 satisfying that X ε,η converges uniformly to X in each compact subset of R n \ ∑ when ε, η → 0. We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of X ε.η . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.