The number of limit cycles of a quintic polynomial system

DOI10.1016/j.camwa.2008.10.079zbMath1165.34332OpenAlexW2074494063MaRDI QIDQ1029856

Hamid R. Z. Zangeneh, Nemat Nyamoradi, Ali Atabaigi

Publication date: 13 July 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.10.079

zbMATH Keywords

limit cycleszeros of abelian integrals

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (18)

The Number of Limit Cycles for a Class of Cubic Systems with Multiple Parameters ⋮ Bifurcation of Limit Cycles from the Center of a Family of Cubic Polynomial Vector Fields ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ Bounding the Number of Zeros of Abelian Integral for a Class of Integrable non-Hamilton System ⋮ Limit cycles bifurcating from a perturbed quartic center ⋮ Upper bounds for the number of zeroes for some abelian integrals ⋮ Poincaré-Pontryagin-Melnikov functions for a type of perturbed degenerate Hamiltonian equations ⋮ On the Chebyshev property for a new family of functions ⋮ On the number of limit cycles of a perturbed cubic polynomial differential center ⋮ BIFURCATION OF LIMIT CYCLES FROM THE GLOBAL CENTER OF A CLASS OF INTEGRABLE NON-HAMILTON SYSTEMS ⋮ LIMIT CYCLE BIFURCATIONS OF TWO KINDS OF POLYNOMIAL DIFFERENTIAL SYSTEMS ⋮ The number of limit cycles of a polynomial system on the plane ⋮ Limit cycles of a class of Hilbert's sixteenth problem presented by fractional differential equations ⋮ The number of limit cycles from a cubic center by the Melnikov function of any order ⋮ The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points ⋮ Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves ⋮ Poincaré bifurcations of two classes of polynomial systems ⋮ On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree

Cites Work

• Global bifurcation of limit cycles in a family of polynomial systems
• The Chebyshev property of elliptic integrals
• On the nonoscillation of elliptic integrals
• Limit cycles of a perturbed cubic polynomial differential center
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• On the nonexistence, existence and uniqueness of limit cycles
• Averaging analysis of a perturbated quadratic center
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