Limit cycle bifurcations of some Liénard systems

DOI10.1016/j.jmaa.2009.12.035zbMath1200.34036OpenAlexW2092687100MaRDI QIDQ2268083

Valery G. Romanovski, Junmin Yang, Mao'an Han

Publication date: 10 March 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.12.035

zbMATH Keywords

bifurcationlimit cyclepolynomial systemDouble homoclinic 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)

Related Items (26)

Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems ⋮ Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system ⋮ Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop ⋮ Limit cycles of generalized Liénard polynomial differential systems via averaging theory ⋮ Limit cycle bifurcations in a kind of perturbed Liénard system ⋮ Hopf Bifurcation of Z2-Equivariant Generalized Liénard Systems ⋮ Hilbert's sixteenth problem for polynomial Liénard equations ⋮ Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops ⋮ Bifurcation of limit cycles from a Liénard system with asymmetric figure eight-loop case ⋮ 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 of some polynomial Liénard systems ⋮ Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator ⋮ Limit cycles of a class of Liénard systems with restoring forces of seventh degree ⋮ On limit cycles near two centres and a double homoclinic loop in Liénard differential system ⋮ ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS ⋮ On the independent perturbation parameters and the number of limit cycles of a type of Liénard system ⋮ Maximum Number of Small Limit Cycles in Some Rational Liénard Systems with Cubic Restoring Terms ⋮ New lower bounds for the Hilbert number of polynomial systems of Liénard type ⋮ Limit cycles near an eye-figure loop in some polynomial Liénard systems ⋮ Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7 ⋮ LIMIT CYCLE BIFURCATIONS OF SOME LIÉNARD SYSTEMS WITH A NILPOTENT CUSP ⋮ Bifurcations of limit cycles in complex networks of Hamiltonian systems and Lloyd's conjecture ⋮ NUMBER OF LIMIT CYCLES OF SOME POLYNOMIAL LIÉNARD SYSTEMS ⋮ Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

Cites Work

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• Limit cycles in generalized Liénard systems
• Limit cycles near homoclinic and heteroclinic loops
• On the number of limit cycles of a cubic near-Hamiltonian system
• On Hopf cyclicity of planar systems
• Symmetry in planar dynamical systems
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Some bifurcation methods of finding limit cycles
• More limit cycles than expected in Liénard equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS

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