Piecewise linear differential systems with only centers can create limit cycles?

Autor(es)

Llibre, Jaume ^[1] ; Teixeira, Marco Antonio ^[2]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 91, n. 1, p. 249-255, JAN 2018.
• Citações Web of Science: 4

Resumo

In this article, we study the continuous and discontinuous planar piecewise differential systems formed only by linear centers separated by one or two parallel straight lines. When these piecewise differential systems are continuous, they have no limit cycles. Also if they are discontinuous separated by a unique straight line, they do not have limit cycles. But when the piecewise differential systems are discontinuous separated two parallel straight lines, we show that they can have at most one limit cycle, and that there exist such systems with one limit cycle. (AU)

• 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