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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: PHYSICA D-NONLINEAR PHENOMENA; v. 407, JUN 2020.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 19/05657-4 - Bifurcations of nested invariant tori and invariant sets of Lotka-Volterra differential systems
• Grantee: Murilo Rodolfo Cândido
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor