On the zeros of the Abelian integrals for a class of Liénard systems

DOI10.1016/j.physleta.2006.05.031zbMath1142.34327OpenAlexW2045906855MaRDI QIDQ942498

Yu-Chu Tian, Tonghua Zhang, Moses O. Tadé

Publication date: 5 September 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://eprints.qut.edu.au/23331/1/23331.pdf

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (19)

Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop. II ⋮ The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle ⋮ On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation ⋮ Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods ⋮ Bifurcation of limit cycles from a hyper-elliptic Hamiltonian system with a double heteroclinic loops ⋮ The perturbation of a class of hyper-elliptic Hamilton system with a double eight figure loop ⋮ Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles ⋮ Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles ⋮ The cyclicity of period annuli of a class of quintic Hamiltonian systems ⋮ Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems ⋮ Linear estimate of the number of limit cycles for a class of nonlinear systems ⋮ Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop ⋮ Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms ⋮ Poincaré bifurcation of limit cycles from a Liénard system with a homoclinic loop passing through a nilpotent saddle ⋮ Bifurcations of limit cycles in a class of hyper-elliptic Liénard systems ⋮ The monotonicity of the ratio of two Abelian integrals ⋮ BIFURCATIONS OF LIMIT CYCLES FROM A QUINTIC HAMILTONIAN SYSTEM WITH A FIGURE DOUBLE-FISH

Cites Work

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• The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Limit cycles in a class of hybrid dynamical systems
• Twelve limit cycles in a cubic order planar system with \(Z_2\) symmetry
• Perturbation from an asymmetric cubic Hamiltonian
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Extremum seeking for limit cycle minimization
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
• Mathematical problems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• On Second Order Bifurcations of Limit Cycles
• LINEAR SYSTEMS, LIMIT CYCLES, MELNIKOV THEORY, AND THE METHOD OF SLOWLY VARYING AMPLITUDE AND PHASE
• Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop
• Three limit cycles for a first-order exothermic chemical reaction in a continuous stirred-tank reactor
• The infinitesimal 16th Hilbert problem in the quadratic case
• Fast computation of limit cycles in an industrial application
• Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles
• Erratum to ``Functions operating on modulation spaces and nonlinear dispersive equations

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