ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR

DOI10.1142/S0218127404011132zbMath1070.34048OpenAlexW2059049876MaRDI QIDQ4655700

Xian-feng Chen, Mao'an Han, Yu-Hai Wu

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127404011132

zbMATH Keywords

limit cyclesHopf bifurcationsmall perturbationsaddle-loop bifurcationRayleigh-Liénard 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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Cites Work

• On the stability of double homoclinic and heteroclinic cycles.
• Small Amplitude Limit Cycles Of The Generalized Mixed Rayleigh-Liénard Oscillator
• THE NUMBER OF LIMIT CYCLES FOR THE GENERALIZED MIXED RAYLEIGH-LIÉNARD OSCILLATOR
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• The limit cycles of the generalized Rayleigh-Liénard oscillator
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem
• A generalization of the method of harmonic balance