On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones

Autor(es)

Silva Lima, Mauricio Firmino ^[1] ; Pessoa, Claudio ^[2] ; Pereira, Weber F. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, BR-09210170 Santo Andre, SP - Brazil

^[2] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 25, n. 4 APR 2015.
• Citações Web of Science: 1

Resumo

Lima and Llibre {[}2012] have studied a class of planar continuous piecewise linear vector fields with three zones. Using the Poincare map, they proved that this class admits always a unique limit cycle, which is hyperbolic. The class studied in {[}Lima \& Llibre, 2012] belongs to a larger set of planar continuous piecewise linear vector fields with three zones that can be separated into four other classes. Here, we consider some of these classes and we prove that some of them always admit a unique limit cycle, which is hyperbolic. However we find a class that does not have limit cycles. (AU)

• Processo FAPESP: 13/15941-5 - Sistemas dinâmicos contínuos e descontínuos
• Beneficiário: Maurício Firmino Silva Lima
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/13152-8 - Teoria qualitativa de campos de vetores polinomiais
• Beneficiário: Cláudio Gomes Pessoa
• Modalidade de apoio: Auxílio à Pesquisa - Regular