Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles

DOI10.1006/jdeq.2000.3828zbMath0986.34029OpenAlexW2032833409MaRDI QIDQ5931934

Mao'an Han

Publication date: 13 May 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3828

zbMATH Keywords

limit cyclesbifurcationnonlinear oscillationsordinary differential equationsMelnikov function

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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)

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Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems ⋮ LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER ⋮ Bifurcations of traveling wave solutions of a generalized Burgers-Fisher equation ⋮ Global bifurcation of a perturbed double-homoclinic loop ⋮ Bounding the number of zeros of certain abelian integrals ⋮ BIFURCATION OF MULTIPLE LIMIT CYCLES FOR A ROTOR-ACTIVE MAGNETIC BEARINGS SYSTEM WITH TIME-VARYING STIFFNESS ⋮ Melnikov function and limit cycle bifurcation from a nilpotent center ⋮ HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS ⋮ THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER CUBIC PERTURBATIONS ⋮ THE ABELIAN INTEGRALS OF A ONE-PARAMETER HAMILTONIAN SYSTEM UNDER POLYNOMIAL PERTURBATIONS ⋮ A Chebyshev criterion for Abelian integrals

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