Preservation of Hopf bifurcation for neutral delay-differential equations by \(\theta\)-methods
type: Item
instance of: scholarly article
title: Preservation of Hopf bifurcation for neutral delay-differential equations by \(\theta\)-methods
zbMATH Open document ID: 1266.65117
author: Huan Su
author: Wenxue Li
author: Xiaohua Ding
published in: Journal of Computational and Applied Mathematics
publication date: 2013-04-18T00:00:00Z
review text: The authors discuss the behaviour of the classical \(\theta\)-method when applied to a certain neutral delay differential equation that exhibits a Hopf bifurcation. In particular, they demonstrate that the \(\theta\)-method preserves the bifurcation and the asymptotic stability of the exact solution if the step size \(h\) satisfies \(h = 1/m\) and \(m \in \mathbb N\) is sufficiently large. A part of the paper is devoted to showing how large \(m\) must be chosen to this end for any given value of the parameter \(\theta\). In particular, it turns out that any \(m \geq 1\) can be used in the practically very important case \(\theta = 1/2\).
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 6155455
zbMATH Keywords: neutral delay-differential equations
zbMATH Keywords: \(\theta\)-method
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Neimark-Sacker bifurcation
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: j.cam.2013.01.020
OpenAlex ID: W2085717534
DOI: 10.1016/J.CAM.2013.01.020
description: scientific article; zbMATH DE number 6155455