Numerical Hopf bifurcation for a class of delay differential equations
type: Item
instance of: scholarly article
title: Numerical Hopf bifurcation for a class of delay differential equations
zbMATH Open document ID: 0946.65065
DOI: 10.1016/S0377-0427(99)00181-8
author: Volker Wulf
author: Neville J. Ford
published in: Journal of Computational and Applied Mathematics
publication date: 2000-10-10T00:00:00Z
review text: Parameter-dependent delay differential equations (DDEq) \[ x'(t)=f(x(t),x(t-\tau),\lambda),\quad \lambda\in \mathbb{R},\quad t\geq 0,\quad x(t)=\varphi(t),\quad -\tau\leq t\leq 0,\quad \tau>0, \] (\(\varphi\) is the continuous initial function) containing a Hopf bifurcation are considered. In previous work [\textit{N. J. Ford, V. Wulf}, The use of boundary locus plots in the identification of bifurcating points in the numerical approximation of delay differential equations, MCCM Tech. Report 322, Manchester Univ., ISSN 1360-1725 (1998)] the authors have shown that strictly stable linear multistep methods applied to DDEqs with Hopf bifurcation yield difference equations which contain a Hopf bifurcation of the same type. The results of the present article extend the authors' previous analysis relating to the discretization of the delay logistic equation to a wider class of problems.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K28
zbMATH DE Number: 1423347
zbMATH Keywords: delay differential equations
zbMATH Keywords: numerical methods
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: linear multistep methods
zbMATH Keywords: difference equations
zbMATH Keywords: delay logistic equation
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00181-8
OpenAlex ID: W2067450357
description: scientific article; zbMATH DE number 1423347