Creation-annihilation process of limit cycles in the Rayleigh-Duffing oscillator

DOI10.1007/s11071-012-0508-xzbMath1268.34067OpenAlexW2040050692MaRDI QIDQ354293

Mohammad Hasan, M. Dambrine

Publication date: 18 July 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0508-x

zbMATH Keywords

limit cycleglobal bifurcationRayleigh-Duffing oscillatorvan der Pol-Duffing oscillator

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

On the truly nonlinear oscillator with positive and negative damping ⋮ On the number of limit cycles of a class of Liénard-Rayleigh oscillators ⋮ Chaos of the Rayleigh-Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation ⋮ Dynamics of polynomial Rayleigh-Duffing system near infinity and its global phase portraits with a center ⋮ Limit cycle oscillations in a mechanical system under fractional-order Liénard type nonlinear feedback ⋮ The focus case of a nonsmooth Rayleigh-Duffing oscillator ⋮ On the dynamics of the Rayleigh-Duffing oscillator ⋮ Liouvillian integrability of a general Rayleigh-Duffing oscillator ⋮ The saddle case of Rayleigh-Duffing oscillators ⋮ Non-existence, existence, and uniqueness of limit cycles for a generalization of the van der Pol-Duffing and the Rayleigh-Duffing oscillators

Uses Software

• AUTO
• AUTO-86

Cites Work

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