Liénard equation and its generalizations

In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a generalization of such systems and we study their center conditions and the number of small-amplitude limit cycles that can bifurcate from the origi...

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Bibliographic Details
Author: Giné, Jaume
Format: article
Status:Versión aceptada para publicación
Publication Date:2017
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/62977
Online Access:https://doi.org/10.1142/S021812741750081X
http://hdl.handle.net/10459.1/62977
Access Level:Open access
Keyword:Center problem
Analytic integrability
Liénard differential systems
Description
Summary:In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a generalization of such systems and we study their center conditions and the number of small-amplitude limit cycles that can bifurcate from the origin. Computing the focal values and using Gröbner bases we find the center conditions for such systems up to a certain degree. We also establish a conjecture about the center conditions for such systems when they have arbitrary degree.