The limit cycles in a generalized Rayleigh-Liénard oscillator

DOI10.3934/dcds.2023014zbMath1525.34060arXiv2203.02829OpenAlexW4322389111MaRDI QIDQ6041193

Iliya D. Iliev, Lyubomir Gavrilov

Publication date: 26 May 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.02829

zbMATH Keywords

limit cyclesBautin idealabelian integralsNakayama lemmaMelnikov functions of arbitrary order

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) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Cites Work

• On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
• Center conditions at infinity for Abel differential equations
• On the nonoscillation of elliptic integrals
• Higher order bifurcations of limit cycles
• Perturbations of quadratic centers
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• On the cubic perturbations of the symmetric 8-loop Hamiltonian
• On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields
• Cyclicity of period annuli and principalization of Bautin ideals
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• ON THE STUDY OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIENARD OSCILLATOR
• On Second Order Bifurcations of Limit Cycles
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Hilbert’s 16th problem on a period annulus and Nash space of arcs
• Lower bounds for the number of limit cycles in a generalised Rayleigh–Liénard oscillator
• Perturbation theory of the quadratic Lotka–Volterra double center
• Complex zeros of an elliptic integral

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