How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation?
type: Item
instance of: scholarly article
title: How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation?
zbMATH Open document ID: 0971.65068
DOI: 10.1016/S0377-0427(00)00473-8
author: Volker Wulf
author: Neville J. Ford
published in: Journal of Computational and Applied Mathematics
publication date: 2001-02-18T00:00:00Z
review text: This paper considers the behaviour of \(\theta\)-methods applied with a constant stepsize of integer fractions to delay differential equations undergoing a Hopf bifurcation. Three different approaches are adopted (a boundary locus approach, a direct bifurcation analysis of the difference scheme using a fixed-point iteration and a projection approach) which lead to the conclusion that \(\theta\)-methods retain Hopf bifurcations and preserve their type for sufficiently small values of the stepsize.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K28
zbMATH DE Number: 1566017
zbMATH Keywords: theta method
zbMATH Keywords: mesh refinement
zbMATH Keywords: delay differential equations
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: difference scheme
zbMATH Keywords: fixed-point iteration
reviewed by: Kevin Burrage
describes a project that uses: PDDE-CONT
MaRDI profile type: Publication
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full work available at URL: s0377-0427(00)00473-8
OpenAlex ID: W2067576443
description: scientific article; zbMATH DE number 1566017