The number of limit cycles of a class of polynomial differential systems

DOI10.1016/j.na.2011.08.037zbMath1235.34100OpenAlexW1971900455MaRDI QIDQ644205

Haiyan Yao, Mao'an Han

Publication date: 3 November 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.08.037

zbMATH Keywords

limit cyclescyclicityargument principlefirst-order Melnikov function

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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (10)

The number of limit cycles in perturbations of polynomial systems with multiple circles of critical points ⋮ The Number of Limit Cycles for a Class of Cubic Systems with Multiple Parameters ⋮ Limit cycle bifurcations in perturbations of planar piecewise smooth systems with multiply lines of critical points ⋮ Bounding the Number of Zeros of Abelian Integral for a Class of Integrable non-Hamilton System ⋮ On the number of limit cycles of a perturbed cubic polynomial differential center ⋮ Abelian integrals and limit cycles for a class of cubic polynomial vector fields of Lotka-Volterra type with a rational first integral of degree two ⋮ Poincaré bifurcations of two classes of polynomial systems ⋮ Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center ⋮ Limit Cycle Bifurcations in a Class of Piecewise Smooth Polynomial Systems ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems

Cites Work

• Unnamed Item
• Limit cycles of cubic polynomial vector fields via the averaging theory
• The number of limit cycles of a quintic polynomial system with center
• Limit cycles of a perturbed cubic polynomial differential center
• On the nonexistence, existence and uniqueness of limit cycles
• Averaging analysis of a perturbated quadratic center

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