Sharp bound of the number of zeros for a Liénard system with a heteroclinic loop

DOI10.1155/2021/6625657zbMath1465.34043OpenAlexW3124765729MaRDI QIDQ2657439

Guoping Pang, Junning Cai, Minzhi Wei

Publication date: 12 March 2021

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/6625657

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) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Cites Work

• Unnamed Item
• 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
• Bounding the number of zeros of certain abelian integrals
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11
• Bifurcations on a five-parameter family of planar vector field
• On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop
• Coexistence of the solitary and periodic waves in convecting shallow water fluid
• Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop. II
• Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles
• Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop
• BIFURCATIONS OF LIMIT CYCLES FROM A QUINTIC HAMILTONIAN SYSTEM WITH A FIGURE DOUBLE-FISH
• A Chebyshev criterion for Abelian integrals
• On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
• 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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