The third order Melnikov function of a quadratic center under quadratic perturbations

DOI10.1016/j.jmaa.2006.09.008zbMath1125.34022OpenAlexW2051702433MaRDI QIDQ879128

Jiazhong Yang, Adriana Buică, Armengol Gasull

Publication date: 4 May 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.09.008

zbMATH Keywords

limit cyclesbifurcationquadratic systemshigh order Melnikov functions

Mathematics Subject Classification ID

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)

Related Items (19)

The third order Melnikov function of a cubic integrable system under quadratic perturbations ⋮ Using Melnikov functions of any order for studying limit cycles ⋮ Center conditions and limit cycles for the perturbation of an elliptic sector ⋮ Limit cycles of discontinuous perturbed quadratic center via the second order averaging method ⋮ High-order Melnikov method for time-periodic equations ⋮ Chaotic heteroclinic tangles with the degenerate Melnikov function ⋮ Melnikov analysis in a cubic system with a multiple line of critical points ⋮ Melnikov analysis of a perturbed integrable non-Hamiltonian system ⋮ Homoclinic solutions for a forced generalized Liénard system ⋮ An estimation for the number of limit cycles in a Liénard-like perturbation of a quadratic nonlinear center ⋮ The Number of Limit Cycles Bifurcating from a Quadratic Reversible Center ⋮ Homoclinic solutions for a forced Liénard type system ⋮ The number of limit cycles from a cubic center by the Melnikov function of any order ⋮ A class of reversible quadratic systems with piecewise polynomial perturbations ⋮ Second Order Melnikov Functions of Piecewise Hamiltonian Systems ⋮ Periodic orbits from second order perturbation via rational trigonometric integrals ⋮ The center conditions for a perturbed cubic center via the fourth-order Melnikov function ⋮ Eventually vanishing solutions of a forced Liénard system ⋮ Essential perturbations of polynomial vector fields with a period annulus

Cites Work

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• Perturbations of quadratic centers
• On the distribution and number of limit cycles for quadratic systems with two foci
• A survey of quadratic systems
• Mathematical problems
• 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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