Bifurcation of limit cycles from a polynomial non-global center

DOI10.1007/s10884-008-9112-7zbMath1166.34017OpenAlexW2039977986MaRDI QIDQ957746

Armengol Gasull, Joan Torregrosa, Rafel Prohens

Publication date: 1 December 2008

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-008-9112-7

zbMATH Keywords

bifurcationlimit cycleAbelian integralpolynomial differential system16-th Hilbert's problem

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)

Related Items (21)

The number of limit cycles in perturbations of polynomial systems with multiple circles of critical points ⋮ The third order Melnikov function of a cubic integrable system under quadratic perturbations ⋮ Simultaneous bifurcation of limit cycles from a linear center with extra singular points ⋮ Limit cycle bifurcations of a planar near-integrable system with two small parameters ⋮ Limit cycle bifurcations in perturbations of planar piecewise smooth systems with multiply lines of critical points ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ Bounding the Number of Zeros of Abelian Integral for a Class of Integrable non-Hamilton System ⋮ Limit cycles bifurcating from a perturbed quartic center ⋮ Upper bounds for the number of zeroes for some abelian integrals ⋮ Poincaré-Pontryagin-Melnikov functions for a type of perturbed degenerate Hamiltonian equations ⋮ Limit cycles appearing from the perturbation of a system with a multiple line of critical points ⋮ On the number of limit cycles of a perturbed cubic polynomial differential center ⋮ A note on the period function for certain planar vector fields ⋮ The number of limit cycles of a polynomial system on the plane ⋮ The number of limit cycles from a cubic center by the Melnikov function of any order ⋮ Cyclicity of some Liénard systems ⋮ Poincaré bifurcations of two classes of polynomial systems ⋮ The center conditions for a perturbed cubic center via the fourth-order Melnikov function ⋮ BIFURCATION OF LIMIT CYCLES BY PERTURBING A PERIODIC ANNULUS WITH MULTIPLE CRITICAL POINTS ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems ⋮ On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree

Cites Work

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• Global bifurcation of limit cycles in a family of polynomial systems
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Weak focus, limit cycles, and bifurcations for bounded quadratic systems
• Limit cycles of a perturbed cubic polynomial differential center
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Averaging analysis of a perturbated quadratic center

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