Naimark-Sacker bifurcations in the Euler method for a delay differential equation
type: Item
instance of: scholarly article
title: Naimark-Sacker bifurcations in the Euler method for a delay differential equation
zbMATH Open document ID: 0918.65054
DOI: 10.1023/A:1022373309178
author: K. Appert
published in: BIT
publication date: 1999-08-17T00:00:00Z
review text: This paper deals with an application of the Euler method to the equation \(u'(t)=-\mu u(t-1)(1-u^2(t))\), \(\mu>0\), which has a Hopf bifurcation at \(\mu=\pi/2\). The author proves that such bifurcations occur in the discretization by using the center manifold theorem and the Naimark-Sacker theorem [cf. \textit{G. Iooss}, Bifurcation of maps and applications, North-Holland, Amsterdam (1979; Zbl 0408.58019)].
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1275245
zbMATH Keywords: delay differential equation
zbMATH Keywords: Euler method
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: center manifold theorem
zbMATH Keywords: Naimark-Sacker theorem
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: a:1022373309178
OpenAlex ID: W126538223
description: scientific article; zbMATH DE number 1275245