LIMIT CYCLE BIFURCATIONS OF SOME LIÉNARD SYSTEMS WITH A NILPOTENT CUSP

DOI10.1142/S0218127410028045zbMath1208.34049OpenAlexW2092620540MaRDI QIDQ3086282

Junmin Yang, Mao'an Han

Publication date: 30 March 2011

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127410028045

zbMATH Keywords

cuspLiénard systemlimit cyclenilpotent singular point

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 (10)

Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops ⋮ Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems ⋮ Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop ⋮ LIMIT CYCLE BIFURCATIONS OF A KIND OF LIÉNARD SYSTEM WITH A HYPOBOLIC SADDLE AND A NILPOTENT CUSP ⋮ Limit cycles in a quartic system with a third-order nilpotent singular point ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator ⋮ On limit cycles near two centres and a double homoclinic loop in Liénard differential system ⋮ New lower bounds for the Hilbert number of polynomial systems of Liénard type

Cites Work

• Melnikov function and limit cycle bifurcation from a nilpotent center
• On Hopf cyclicity of planar systems
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Limit cycle bifurcations of some Liénard systems
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• The number of small-amplitude limit cycles of Liénard equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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