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

Autor(es)

Carvalho, Tiago ; Euzebio, Rodrigo D. ; Teixeira, Marco Antonto ; Tonon, Durval Jose

• Tipo de documento: Artigo Científico
• Fonte: IMA JOURNAL OF APPLIED MATHEMATICS; v. 82, n. 3, p. 561-578, JUN 2017.
• Citações Web of Science: 0

Resumo

We consider a piecewise smooth vector field in R-3, 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. (AU)

• Processo FAPESP: 14/18508-3 - Conjuntos minimais de sistemas suaves por partes em dimensão 3
• Beneficiário: Rodrigo Donizete Euzébio
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 13/25828-1 - Conjuntos minimais e variedades invariantes em sistemas suaves por partes
• Beneficiário: Rodrigo Donizete Euzébio
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 14/02134-7 - Teoria qualitativa e bifurcações de campos de vetores suaves por partes
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular