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

DOI10.1016/j.physd.2020.132458zbMath1496.34062OpenAlexW3011625429MaRDI QIDQ2115551

Jaume Llibre, Claudia Valls, Murilo R. Cândido

Publication date: 17 March 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2020.132458

zbMATH Keywords

limit cyclesvan der Pol-Duffing oscillatorRayleigh-Duffing oscillator, global phase portraits

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (10)

On an integrability criterion for a family of cubic oscillators ⋮ On the number of limit cycles of a class of Liénard-Rayleigh oscillators ⋮ A van der Pol-Duffing oscillator with indefinite degree ⋮ Oscillations on one dimensional time dependent center manifolds: algebraic curves approach ⋮ Chaos of the Rayleigh-Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation ⋮ On the existence and uniqueness of limit cycles for hybrid oscillators ⋮ Linearizabiliy and Lax representations for cubic autonomous and non-autonomous nonlinear oscillators ⋮ Linearizability conditions for the Rayleigh-like oscillators ⋮ ZERO BIFURCATION DIAGRAMS FOR ABELIAN INTEGRALS: A STUDY ON HIGHER-ORDER HYPERELLIPTIC HAMILTONIAN SYSTEMS WITH THREE PERTURBATION PARAMETERS ⋮ Global dynamics of hybrid van der Pol-Rayleigh oscillators

Cites Work

• Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator
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• Quadratic Liénard equations with quadratic damping
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• Qualitative theory of planar differential systems
• Cubic Lienard equations with linear damping
• DYNAMICS OF ELASTIC EXCITABLE MEDIA
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
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