Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
Carregando...
Data
2017-01-01
Autores
Carvalho, Tiago [UNESP]
Euźebio, Rodrigo D.
Teixeira, Marco Antonto
Tonon, Durval Jośe
Título da Revista
ISSN da Revista
Título de Volume
Editor
Resumo
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.
Descrição
Palavras-chave
Bifurcation, Limit cycles, Periodic solutions, Piecewise smooth vector fields
Como citar
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 82, n. 3, p. 561-578, 2017.