The number of limit cycles from a cubic center by the Melnikov function of any order

DOI10.1016/j.jde.2019.08.053zbMath1446.34056OpenAlexW2972560302MaRDI QIDQ2279552

Peixing Yang, Jiang Yu

Publication date: 13 December 2019

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

Full work available at URL: https://doi.org/10.1016/j.jde.2019.08.053

zbMATH Keywords

limit cyclesbifurcationgeneratorsMelnikov functions

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (11)

The number of limit cycles for some polynomial systems with multiple parameters ⋮ Limit Cycles from Hopf Bifurcation in Nongeneric Quadratic Reversible Systems with Piecewise Perturbations ⋮ Limit cycle bifurcations of a planar near-integrable system with two small parameters ⋮ The Number of Limit Cycles for a Class of Cubic Systems with Multiple Parameters ⋮ Melnikov analysis in a cubic system with a multiple line of critical points ⋮ Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers ⋮ Melnikov analysis of a perturbed integrable non-Hamiltonian system ⋮ Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis ⋮ The number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order ⋮ Bifurcation of limit cycles in a piecewise smooth near-integrable system ⋮ Bifurcation of periodic orbits of periodic equations with multiple parameters by averaging method

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