Analysis of global bifurcation for a class of systems of degree five
type: Item
instance of: scholarly article
title: Analysis of global bifurcation for a class of systems of degree five
zbMATH Open document ID: 0994.34027
author: Wang Xian
author: Jiang Jifa
author: Yan Ping
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-03T00:00:00Z
review text: Consider the two-dimensional system \[ dx/dt= y,\quad dy/dt= -x-(x^2- a)(1+ y^2)y,\tag{\(*\)} \] where \(a\) is a parameter. The authors give a complete bifurcation analysis of \((*)\) and prove that \((*)\) has a unique stable limit cycle for some parameter interval which is generated by a Hopf and a separatrix loop bifurcation correspondingly.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1218604
zbMATH Keywords: global bifurcation
zbMATH Keywords: limit cycle
zbMATH Keywords: separatrix loop bifurcation
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5546
OpenAlex ID: W1974788414
cites work: Q5335550
cites work: Q4004269
cites work: Periodic solutions of generalized Liénard equations
cites work: Q3715459
cites work: Q3273432
cites work: Q4849001
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cites work: Stability theory for ordinary differential equations
DOI: 10.1006/JMAA.1997.5546
description: scientific article; zbMATH DE number 1218604