Melnikov function and limit cycle bifurcation from a nilpotent center

DOI10.1016/j.bulsci.2006.11.006zbMath1143.37043OpenAlexW2027696719MaRDI QIDQ924306

Jiao Jiang, Mao'an Han

Publication date: 15 May 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.11.006

zbMATH Keywords

Hopf bifurcationMelnikov functionnilpotent centernear-Hamiltonian systems

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (12)

Bifurcation of a piecewise smooth cubic system via expansion of Melnikov function ⋮ Computation of expansion coefficients of Melnikov functions near a nilpotent center ⋮ On the number of zeros of abelian integral for some Liénard system of type \((4,3)\) ⋮ Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop ⋮ On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ HOPF BIFURCATION OF LIÉNARD SYSTEMS BY PERTURBING A NILPOTENT CENTER ⋮ On the Distribution of Limit Cycles in a Liénard System with a Nilpotent Center and a Nilpotent Saddle ⋮ LIMIT CYCLE BIFURCATIONS OF SOME LIÉNARD SYSTEMS WITH A NILPOTENT CUSP ⋮ Bifurcations in a Cubic System with a Degenerate Saddle Point ⋮ BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP ⋮ Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

Cites Work

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

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