The number of limit cycles of a polynomial system on the plane

DOI10.1155/2013/482850zbMath1300.34068OpenAlexW2097262626WikidataQ58916389 ScholiaQ58916389MaRDI QIDQ2015582

Chao Liu, Mao'an Han

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/482850

zbMATH Keywords

limit cycleabelian integral16-th Hilbert's problemperturbed planar system

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)

Related Items (1)

The Number of Limit Cycles for a Class of Cubic Systems with Multiple Parameters

Cites Work

• Upper bounds for the number of zeroes for some abelian integrals
• Global bifurcation of limit cycles in a family of polynomial systems
• Limit cycles bifurcating from a perturbed quartic center
• Limit cycles appearing from the perturbation of a system with a multiple line of critical points
• Bifurcation of limit cycles from a polynomial non-global center
• The number of limit cycles of a quintic polynomial system
• Limit cycles of a perturbed cubic polynomial differential center
• Some unsolved problems in the theory of differential equations and mathematical physics
• On the nonexistence, existence and uniqueness of limit cycles
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Averaging analysis of a perturbated quadratic center

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