Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder

Autor(es)

Buzzi, C. A. ^[1] ; Euzebio, R. D. ^[1] ; Mereu, A. C. ^[2]

Afiliação do(s) autor(es)

^[1] IBILCE UNESP Univ Estadual Paulista, Dept Math, Rua Cristovao Colombo 2265, BR-15054000 Selo Jose De Rio Preto, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Phys Chem & Math, BR-18052780 Sorocaba, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 140, n. 5, p. 519-540, JUN 2016.
• Citações Web of Science: 0

Resumo

Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in R-3. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin bifurcation function for C-0 perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in R-3 and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved. (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: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• 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