Global bifurcations of limit and separatrix cycles in a generalized Liénard system
type: Item
instance of: scholarly article
title: Global bifurcations of limit and separatrix cycles in a generalized Liénard system
zbMATH Open document ID: 1082.34035
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-11-22T00:00:00Z
review text: This paper is concerned with periodic orbits and separatrix cycles in a particular kind of cubic differential equations in \(\mathbb R^2\) -- the so-called Kukles systems. Using field-rotation parameters, the authors show that three different types of those equations can be distinguished. One type corresponds to a generalized Liénard equation. For that kind, the periodic orbits and separatrix cycles are studied in detail. In particular, all possible separatrix and limit cycles are listed.
reviewed by: Jürgen Knobloch
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 2117569
zbMATH Keywords: cubic dynamical system
zbMATH Keywords: field rotation parameters
zbMATH Keywords: limit cycle
zbMATH Keywords: separatrix cycle
zbMATH Keywords: Kukles-type system
author: Valery A. Gaiko
author: W. T. Van Horssen
MaRDI profile type: Publication
full work available at URL: j.na.2004.07.010
OpenAlex ID: W1970280305
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DOI: 10.1016/J.NA.2004.07.010
description: scientific article; zbMATH DE number 2117569