Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field

We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive intege...

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Detalles Bibliográficos
Autores: Carvalho, Tiago [UNESP], Euźebio, Rodrigo D., Teixeira, Marco Antonto, Tonon, Durval Jośe
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/169891
Acceso en línea:http://dx.doi.org/10.1093/imamat/hxx003
http://hdl.handle.net/11449/169891
Access Level:acceso abierto
Palabra clave:Bifurcation
Limit cycles
Periodic solutions
Piecewise smooth vector fields
Descripción
Sumario:We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive integer k, we produce suitable nonlinear small perturbations of the previous model and we obtain piecewise smooth vector fields having exactly k hyperbolic limit cycles instead of the center. Moreover, we also obtain suitable nonlinear small perturbations of the first model and piecewise smooth vector fields having a unique limit cycle of multiplicity k instead of the center. As consequence, the initial model has codimension infinity. Some aspects of asymptotical stability of such system are also addressed in this article.