Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory
type: Item
instance of: scholarly article
title: Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory
zbMATH Open document ID: 0978.34035
author: B. Fiedler
author: Stefan Liebscher
author: James C. Alexander
published in: Journal of Differential Equations
publication date: 2001-03-13T00:00:00Z
review text: Real autonomous systems of ordinary differential equations are considered having a line of equilibria and satisfying additional nondegeneracy conditions. The loss of stability along this line is investigated in cases of one real/a couple of complex conjugate eigenvalues crossing the imaginary axis. Based on the corresponding 2/3-dimensional normal forms the behavior of close trajectories is presented. The investigation of the problem is motivated by several applications.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G40
zbMATH DE Number: 1529992
zbMATH Keywords: generic Hopf bifurcation
zbMATH Keywords: line of equilibria
zbMATH Keywords: nondegeneracy
reviewed by: Péter F. Moson
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3779
OpenAlex ID: W1848162227
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DOI: 10.1006/JDEQ.2000.3779
description: scientific article; zbMATH DE number 1529992