The number of limit cycles in perturbations of polynomial systems with multiple circles of critical points

DOI10.1016/j.jmaa.2016.03.020zbMath1339.34046OpenAlexW2297942503MaRDI QIDQ269430

Yanqin Xiong

Publication date: 18 April 2016

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.2016.03.020

zbMATH Keywords

limit cycleHopf bifurcationMelnikov 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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (6)

Limit cycle bifurcations of a planar near-integrable system with two small 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 ⋮ Simultaneous bifurcation of limit cycles from a cubic piecewise center with two period annuli ⋮ Limit cycle bifurcations for piecewise smooth integrable differential systems ⋮ The number of limit cycles from a cubic center by the Melnikov function of any order

Cites Work

• Upper bounds for the number of zeroes for some abelian integrals
• On the number of limit cycles of a perturbed cubic polynomial differential center
• 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
• The number of limit cycles of a class of polynomial differential systems
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Bifurcation of limit cycles from a polynomial non-global center
• Limit cycles of a perturbed cubic polynomial differential center
• BIFURCATION OF LIMIT CYCLES BY PERTURBING A PERIODIC ANNULUS WITH MULTIPLE CRITICAL POINTS
• The Maximal Number of Limit Cycles in a Family of Polynomial Systems
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Averaging analysis of a perturbated quadratic center

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