Limit cycles in 4-star-symmetric planar piecewise linear systems

Autor(es)

Buzzi, Claudio A. ^[1] ; Medrado, Joao C. ^[2] ; Torregrosa, Joan ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto - Brazil

^[2] Univ Fed Goias, Inst Matemat & Estat, BR-74001970 Goiania, Go - Brazil

^[3] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 268, n. 5, p. 2414-2434, FEB 15 2020.
• Citações Web of Science: 0

Resumo

Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is xy=0. We consider the symmetric case. That is, one vector field defined in the odd quadrants and the other in the even ones. We deal with equilibrium points of center-focus type, with matrices in real Jordan form, in each vector field when the infinity is monodromic. In this case, we provide the center classification at infinity, we prove that the maximum order of a weak focus is five. Moreover, we show the existence of systems exhibiting five limit cycles bifurcating from infinity. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/03352-6 - Ciclos limites em alguns sistemas diferenciais suaves por partes
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático