Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points
type: Item
instance of: scholarly article
title: Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points
zbMATH Open document ID: 0678.65064
DOI: 10.1016/0377-0427(89)90150-7
author: Michael Dellnitz
author: Bodo Werner
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: This interesting paper exploits group theoretical methods to discuss bifurcation phenomena of a system of ordinary differential equations of the form \((1)\quad \dot x=g(x,\lambda)\) satisfying following condition \((2)\quad g(\gamma x,\lambda)=\gamma g(x,\lambda),\) \(\gamma\in \Gamma\). Here \(\gamma\) is an orthogonal matrix from certain group of \(N\times N\) matrices \(\Gamma\). These matrices are interpreted as some symmetries. The first part of the paper consists of a theoretical background and contains several group theory results especially proved for further applications to the investigated bifurcation problem. The application of these results enables one to detect, to classify, and to compute the bifurcation branches of solutions of (1), (2) for a large class of equations. Examples are from applications to chemical problems.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4111941
zbMATH Keywords: steady state
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: group of symmetry
zbMATH Keywords: group theoretical methods
zbMATH Keywords: bifurcation branches
describes a project that uses: ALCON
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90150-7
OpenAlex ID: W2060571282
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description: scientific article; zbMATH DE number 4111941