Parameter identification on abelian integrals to achieve Chebyshev property

DOI10.3934/dcdsb.2020375zbMath1484.34094OpenAlexW3114653250MaRDI QIDQ2033878

Zhanbo Chen, Xian Bo Sun, Pei Yu

Publication date: 18 June 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2020375

zbMATH Keywords

bifurcationHilbert's 16th problemLienard systemlimit cycle heteroclinic loops

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

Upper Bound on the Number of Zeros of Abelian Integrals for Hyperbolic Hamiltonian Systems of Degree Seven

Uses Software

• DISCOVERER

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithms for computing triangular decomposition of polynomial systems
• Bifurcation of limit cycles from a heteroclinic loop with a cusp
• Bounding the number of zeros of certain abelian integrals
• Normal forms, Melnikov functions and bifurcations of limit cycles
• A unified proof of the weakened Hilbert 16th problem for \(n=2\)
• A complete algorithm for automated discovering of a class of inequality-type theorems
• Limit cycles near homoclinic and heteroclinic loops
• Decomposing polynomial systems into simple systems
• Mathematical problems for the next century
• Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles
• Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points
• A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4
• A criterion for determining the monotonicity of the ratio of two Abelian integrals
• Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4
• Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven
• Complex dynamics in a unified SIR and HIV disease model: a bifurcation theory approach
• Perturbation of a period annulus with a unique two-saddle cycle in higher order Hamiltonian
• Numbers of relative equilibria in the planar four-vortex problem: some special cases
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles
• The monotonicity of the ratio of two Abelian integrals
• A Chebyshev criterion for Abelian integrals
• DYNAMICS OF ELASTIC EXCITABLE MEDIA
• ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
• Strongly nonlinear oscillators. Analytical solutions

This page was built for publication: Parameter identification on abelian integrals to achieve Chebyshev property