Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol-Duffing and the Rayleigh-Duffing oscillators

Autor(es)

Candido, Murilo R. ^[1] ; Llibre, Jaume ^[2] ; Valls, Claudia ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, Rua Sergio Baruque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon - Portugal

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA D-NONLINEAR PHENOMENA; v. 407, JUN 2020.
• Citações Web of Science: 0

Resumo

We study the limit cycles of some cubic family of differential equations, containing the well-known Van der Pol-Duffing and Rayleigh-Duffing oscillators. In particular, we characterize for the class of differential systems here studied the non-existence, existence and uniqueness of limit cycles. Moreover we provide their global phase portraits in the Poincare disk. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 19/05657-4 - Bifurcações de toros invariantes acoplados e conjuntos invariantes no sistema de Lotka-Volterra
• Beneficiário: Murilo Rodolfo Cândido
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado