The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems

DOI10.1016/j.jmaa.2005.04.085zbMath1099.34032OpenAlexW4210804460MaRDI QIDQ819745

Tonghua Zhang, Hong Zang, Mao'an Han

Publication date: 29 March 2006

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.2005.04.085

zbMATH Keywords

limit cycleHamiltonian systemhomoclinic bifurcationHilbert's 16th problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

On the zeros of the Abelian integrals for a class of Liénard systems ⋮ On the bifurcation of double homoclinic loops of a cubic system ⋮ A class of quadratic reversible systems with a center of genus one ⋮ Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

Cites Work

• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Mathematical problems for the next century
• On the number of limit cycles in double homoclinic bifurcations
• Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
• Perturbation from an asymmetric cubic Hamiltonian
• On the stability of double homoclinic and heteroclinic cycles.
• Bifurcations of limit cycles in a cubic system
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM
• Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop
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