Global behavior of limit cycles in rotated vector fields
type: Item
instance of: scholarly article
title: Global behavior of limit cycles in rotated vector fields
zbMATH Open document ID: 0930.34017
published in: Journal of Differential Equations
publication date: 2000-01-31T00:00:00Z
review text: Consider a one-parameter family of vector fields \((*) \;dx/dt =f(x,\lambda)\) where \(f:D\times I \rightarrow \mathbb{R}^2\) is analytic, \(D\) is a connected set of \(\mathbb{R}^2, I\) is an interval. The author gives a definition of rotated vector fields which generalizes the definition given by \textit{L. Perko} [J. Differ. Equations 103, 127-145 (1993; Zbl 0781.34020)]. He studies the global behavior of limit cycles in dependence on \(\lambda\) such as nonintersection, persistence, bifurcation, and limit behavior. The results show that the well-known properties of rotated vector fields remain true under the relaxed definition.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1271363
zbMATH Keywords: limit cycles
zbMATH Keywords: rotated vector fields
author: Maoan Han
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3508
OpenAlex ID: W2055596580
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DOI: 10.1006/JDEQ.1998.3508
description: scientific article; zbMATH DE number 1271363