Constructing global bifurcation diagrams by the parametric representation method
type: Item
instance of: scholarly article
title: Constructing global bifurcation diagrams by the parametric representation method
zbMATH Open document ID: 0940.65051
DOI: 10.1016/S0377-0427(99)00108-9
author: Péter L. Simon
author: Henrik Farkas
author: Mária Wittmann
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-10T00:00:00Z
review text: The problem of determination the number of solutions for the equation \(f_{0}(x)+u_{1}f_{1}(x)+u_{2}f_{2}(x)=0, x\in \mathbb{R},\) as a function of the parameter values \((u_{1},u_{2})\), i.e. construction of the bifurcational curve, is considered. The parametric representation method [\textit{P. Gray} and \textit{S. K. Scott}, Chemical oscillations and instabilities: Nonlinear chemical kinetics, Clarendon Press, Oxford (1994)] is used. This method has two advantages: 1) the singularity set can be easily constructed as a curve parametrized by \(x\), called \(D\)-curve, 2) the solutions belonging to a given parameter pair can be determined by a simple geometric algorithm based on the so-called tangential property.
Mathematics Subject Classification ID: 65H17
zbMATH DE Number: 1367896
zbMATH Keywords: bifurcation diagram
zbMATH Keywords: singularity set
zbMATH Keywords: parametric representation method
zbMATH Keywords: geometric algorithm
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00108-9
OpenAlex ID: W2116527365
description: scientific article; zbMATH DE number 1367896