Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop

DOI10.1016/j.chaos.2011.02.008zbMath1231.34056OpenAlexW2055778140MaRDI QIDQ634902

Junmin Yang, Mao'an Han

Publication date: 17 August 2011

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2011.02.008

zbMATH Keywords

Liénard systembifurcationlimit cyclenear-Hamiltonian system16-th Hilbert's problem

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)

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Cites Work

• Unnamed Item
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• Melnikov function and limit cycle bifurcation from a nilpotent center
• Limit cycles in generalized Liénard systems
• Limit cycles near homoclinic and heteroclinic loops
• Bifurcations on a five-parameter family of planar vector field
• Petrov modules and zeros of abelian integrals
• On Hopf cyclicity of planar systems
• Abelian integrals for cubic vector fields
• 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
• LIMIT CYCLE BIFURCATIONS OF SOME LIÉNARD SYSTEMS WITH A NILPOTENT CUSP
• 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
• 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
• Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop

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