Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis

DOI10.1016/j.chaos.2016.03.007zbMath1355.34058OpenAlexW2297336241MaRDI QIDQ508217

Ji Hua Wang

Publication date: 10 February 2017

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2016.03.007

zbMATH Keywords

interval analysislimit cycleabelian integralsemi-algebraic systemChebyshev criterion

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (7)

Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods ⋮ Poincaré Bifurcation of Some Nonlinear Oscillator of Generalized Liénard Type Using Symbolic Computation Method ⋮ Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop ⋮ Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center ⋮ Abelian integrals in unfoldings of codimension 3 singularities with nilpotent linear parts ⋮ Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4 ⋮ Symbolic computation for the qualitative theory of differential equations

Uses Software

• ISOLATE

Cites Work

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• On the number of zeros of abelian integral for some Liénard system of type \((4,3)\)
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
• Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop
• Bounding the number of zeros of certain abelian integrals
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems
• Limit cycles of differential equations
• Criteria to bound the number of critical periods
• A complete algorithm for counting real solutions of polynomial systems of equations and inequalities.
• Efficient isolation of polynomial's real roots.
• An algorithm for isolating the real solutions of semi-algebraic systems
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• Computer-assisted techniques for the verification of the Chebyshev property of abelian integrals
• Perturbation theory of a symmetric center within Liénard equations
• Abelian integrals and limit cycles for a class of cubic polynomial vector fields of Lotka-Volterra type with a rational first integral of degree two
• The evaluation of the zeros of ill-conditioned polynomials. I, II
• Real Root Isolation of Polynomial Equations Based on Hybrid Computation
• THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE
• A Chebyshev criterion for Abelian integrals
• Limit cycles of the generalized polynomial Liénard differential equations
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• 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
• The period function of hyperelliptic Hamiltonians of degree 5 with real critical points
• Algorithms in real algebraic geometry
• 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

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