Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities

DOI10.1016/j.jmaa.2013.04.076zbMath1314.34065OpenAlexW2000442956MaRDI QIDQ2257506

Rebiha Benterki, Jaume Llibre

Publication date: 25 February 2015

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.2013.04.076

zbMATH Keywords

centerlimit cycleperiodic orbitaveraging methodreversible 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) Averaging method for ordinary differential equations (34C29) 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 (9)

A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities ⋮ Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ On the number of limit cycles bifurcating from a quartic reversible center ⋮ Unnamed Item ⋮ Global planar dynamics with a star node and contracting nonlinearity ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ On the study and application of limit cycles of a kind of piecewise smooth equation ⋮ A new Chebyshev criterion and its application to planar differential systems

Cites Work

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• Limit cycles of differential equations
• Limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method
• Averaging methods for finding periodic orbits via Brouwer degree.
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• The number of limit cycles due to polynomial perturbations of the harmonic oscillator

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