A relation between small amplitude and big limit cycles.

DOI10.1216/rmjm/1021249441zbMath1041.34016OpenAlexW2058897776MaRDI QIDQ1414921

Joan Torregrosa, Armengol Gasull

Publication date: 3 December 2003

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol31-4/CONT31-4/CONT31-4.html

zbMATH Keywords

limit cycledegenerate Hopf bifurcationPoincaré-Melnikov methodFrançoise algorithm

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (16)

On persistent centers ⋮ Medium Amplitude Limit Cycles of Some Classes of Generalized Liénard Systems ⋮ Limit cycles via higher order perturbations for some piecewise differential systems ⋮ On the number of limit cycles bifurcating from a non-global degenerated center ⋮ Cyclicity versus center problem ⋮ Limit cycles in planar piecewise linear differential systems with nonregular separation line ⋮ Minimum number of ideal generators for a linear center perturbed by homogeneous polynomials ⋮ Melnikov analysis of a perturbed integrable non-Hamiltonian system ⋮ Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems ⋮ Medium amplitude limit cycles in second order perturbed polynomial Liénard systems ⋮ Center-Focus Problem for Discontinuous Planar Differential Equations ⋮ The nondegenerate center problem and the inverse integrating factor ⋮ Limit cycles for rigid cubic systems ⋮ Limit cycles of piecewise polynomial differential systems with the discontinuity line \(xy = 0\) ⋮ Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary ⋮ Essential perturbations of polynomial vector fields with a period annulus

Cites Work

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• The number of small-amplitude limit cycles of Liénard equations
• Order of cyclicity of the singular point of lineard's polynomial vector fields
• On Second Order Bifurcations of Limit Cycles
• Successive derivatives of a first return map, application to the study of quadratic vector fields

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