The hyperelliptic limit cycles of the Liénard systems

DOI10.1016/j.jmaa.2010.12.015zbMath1208.34038OpenAlexW1972984593MaRDI QIDQ624612

Xiang Zhang, Xiao Lan Yu

Publication date: 9 February 2011

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.2010.12.015

zbMATH Keywords

Liénard systemalgebraic limit cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (10)

Liouvillian integrability versus Darboux polynomials ⋮ The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Poincaré Bifurcation of Some Nonlinear Oscillator of Generalized Liénard Type Using Symbolic Computation Method ⋮ Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points ⋮ Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator ⋮ Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities ⋮ Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems ⋮ On the number of hyperelliptic limit cycles of Liénard systems ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems

Cites Work

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• Uniqueness of limit cycles for Liénard systems. A generalization of Massera's theorem
• On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
• Relationships between limit cycles and algebraic invariant curves for quadratic systems
• Explicit non-algebraic limit cycles for polynomial systems
• Liénard and Riccati differential equations related via Lie algebras
• Classification of quadratic systems admitting the existence of an algebraic limit cycle
• Planar polynomial vector fields having first integrals and algebraic limit cycles
• The limit cycle of the van der Pol equation is not algebraic
• Coexistence of algebraic and nonalgebraic limit cycles in Kukles systems
• On the 16th Hilbert problem for algebraic limit cycles
• Non-nested configuration of algebraic limit cycles in quadratic systems
• Invariant algebraic curves for the cubic Liénard system with linear damping
• Coexistence of algebraic and non-algebraic limit cycles, explicitly given, using Riccati equations
• More limit cycles than expected in Liénard equations
• NON-ALGEBRAIC LIMIT CYCLES FOR PARAMETRIZED PLANAR POLYNOMIAL SYSTEMS
• On the algebraic limit cycles of Liénard systems
• Limit cycles of the generalized polynomial Liénard differential equations
• Algebraic invariant curves for the Liénard equation
• Algebraic limit cycles in polynomial systems of differential equations
• Uniqueness of algebraic limit cycles for quadratic systems

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