Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems

DOI10.1142/S0218127414500047zbMath1284.34052OpenAlexW2100430328MaRDI QIDQ5407288

Hamid R. Z. Zangeneh, Rasool Kazemi, Hongjian Xi, Xian Bo Sun

Publication date: 7 April 2014

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

Full work available at URL: https://doi.org/10.1142/s0218127414500047

zbMATH Keywords

Liénard systembifurcationlimit cycleMelnikov functionnilpotent saddleheteroclinic loop

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (14)

The monotonicity of the ratio of two hyperelliptic abelian integrals for a class of symmetric potential systems of degree eight ⋮ Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop ⋮ Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8 ⋮ Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ On the number of limit cycles bifurcated from some Hamiltonian systems with a non-elementary heteroclinic loop ⋮ On the Distribution of Limit Cycles in a Liénard System with a Nilpotent Center and a Nilpotent Saddle ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle ⋮ Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven ⋮ Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle ⋮ Symbolic computation for the qualitative theory of differential equations

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