Limit cycles of a class of generalized Liénard polynomial equations

We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.

Bibliographic Details
Authors: Llibre, Jaume|||0000-0002-9511-5999, Makhlouf, Ammar
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:145358
Online Access:https://ddd.uab.cat/record/145358
https://dx.doi.org/urn:doi:10.1007/s10883-014-9253-4
Access Level:Open access
Keyword:Averaging theory
Liénard system
Limit cycles
Polynomial differential systems
Description
Summary:We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.