Computation of expansion coefficients of Melnikov functions near a nilpotent center

DOI10.1016/j.camwa.2012.03.052zbMath1268.34062OpenAlexW2142909104MaRDI QIDQ356092

Junmin Yang, Mao'an Han

Publication date: 25 July 2013

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2012.03.052

zbMATH Keywords

bifurcationlimit cyclenilpotent center

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 (9)

Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops ⋮ LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP ⋮ Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems ⋮ Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\) ⋮ Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7 ⋮ Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a Cuspidal Loop of Order m ⋮ Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

Cites Work

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• Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop
• Melnikov function and limit cycle bifurcation from a nilpotent center
• Limit cycles near homoclinic and heteroclinic loops
• Bifurcations on a five-parameter family of planar vector field
• Complete hyperelliptic integrals of the first kind and their non-oscillation
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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