Global bifurcation studies of a cubic Liénard system
type: Item
instance of: scholarly article
title: Global bifurcation studies of a cubic Liénard system
zbMATH Open document ID: 1464.34061
author: Hebai Chen
author: Huanping Zhu
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-03-01T00:00:00Z
review text: A cubic Liénard system is an important polynomial system. It has attracted the attention of many scholars. For example, the first author of this paper has given a series of papers on the global parameters of the system. In this paper, the three-parameter family of cubic Liénard systems is investigated when the leading coefficient of the restoring is negative. The results show that saddle-node bifurcations, pitchfork bifurcations, Hopf bifurcations, homoclinic bifurcations, and heteroclinic bifurcations will occur by using global analysis. The global bifurcation diagram with global phase portraits depicted in Poincaré disks is given.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 7316428
zbMATH Keywords: cubic Liénard system
zbMATH Keywords: bifurcation
zbMATH Keywords: limit cycle
zbMATH Keywords: homoclinic loop
zbMATH Keywords: global bifurcation diagram
zbMATH Keywords: phase portrait
reviewed by: Chunrui Zhang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2020.124810
OpenAlex ID: W3109529888
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DOI: 10.1016/J.JMAA.2020.124810
description: scientific article; zbMATH DE number 7316428