Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center

DOI10.1142/S0218127415500078zbMath1309.34066MaRDI QIDQ5246671

Fengjie Geng, Hairong Lian

Publication date: 22 April 2015

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

bifurcationlimit cycleAbelian integralsquasi-homogeneous degenerate center

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, 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)

Related Items (4)

On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center ⋮ An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field

Cites Work

• Global bifurcation of limit cycles in a family of polynomial systems
• Limit cycles bifurcating from a perturbed quartic center
• The number of limit cycles of a class of polynomial differential systems
• On the number of limit cycles bifurcating from a non-global degenerated center
• The number of limit cycles of a quintic polynomial system with center
• Limit cycles bifurcating from the period annulus of quasi-homogeneous centers
• BIFURCATION OF LIMIT CYCLES BY PERTURBING A PERIODIC ANNULUS WITH MULTIPLE CRITICAL POINTS
• Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• On the limit cycle bifurcation of a polynomial system from a global center
• Averaging analysis of a perturbated quadratic center

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