ON THE NUMBER OF LIMIT CYCLES FOR A GENERALIZATION OF LIÉNARD POLYNOMIAL DIFFERENTIAL SYSTEMS

DOI10.1142/S021812741350048XzbMath1270.34052OpenAlexW2067119535MaRDI QIDQ2845172

Claudia Valls, Jaume Llibre

Publication date: 22 August 2013

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

Full work available at URL: https://doi.org/10.1142/s021812741350048x

zbMATH Keywords

limit cyclesaveraging theorygeneralized Liénard polynomial differential systems

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

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Limit cycles of generalized Liénard polynomial differential systems via averaging theory, Unnamed Item, On the Number of Limit Cycles of Discontinuous Liénard Polynomial Differential Systems, Unnamed Item, Bifurcation of periodic orbits of periodic equations with multiple parameters by averaging method, Maximum number of limit cycles for generalized Liénard polynomial differential systems, Limit Cycles for a Class of Polynomial Differential Systems Via Averaging Theory

Cites Work

• Averaging methods for finding periodic orbits via Brouwer degree.
• ON THE MAXIMUM NUMBER OF LIMIT CYCLES OF A CLASS OF GENERALIZED LIÉNARD DIFFERENTIAL SYSTEMS
• The number of small-amplitude limit cycles of Liénard equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces