Limit cycle bifurcations of a general Liénard system with polynomial restoring and damping functions
type: Item
instance of: scholarly article
title: Limit cycle bifurcations of a general Liénard system with polynomial restoring and damping functions
zbMATH Open document ID: 1266.34050
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2013-01-11T00:00:00Z
review text: Consider the system \[ \dot{x}=y, \dot{y}=-x(1+\beta_{1}x+\dotsb+\beta_{2l}x^{2l})+y(\alpha_{0}+\alpha_{1}x+\dotsb+\alpha_{2k}x^{2k}). \] By using a canonical system and applying field rotation parameters, the author proves that the system has at most \(k+l\) limit cycles; \(k\) of them are surrounding the origin and the other \(l\) limit cycles surround one by one the other singularities.
reviewed by: M. A. M. Alwash
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6124749
zbMATH Keywords: limit cycle
zbMATH Keywords: Liénard system
zbMATH Keywords: bifurcation
zbMATH Keywords: singular point
author: Valery A. Gaiko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6124749