Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
type: Item
instance of: scholarly article
title: Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
zbMATH Open document ID: 0855.65092
DOI: 10.1016/0377-0427(96)00008-8
author: Tatyana Luzyanina
author: Dirk Roose
published in: Journal of Computational and Applied Mathematics
publication date: 1996-10-07T00:00:00Z
review text: A numerical technique for the stability analysis and the computation of branches of Hopf bifurcation points in systems of nonlinear delay differential equations (DDE) with several constant delays is presented. This technique is implemented within the LOCBIF software package. The stability analysis of a steady-state solution of the system of DDEs is done by the eigenvalues with positive real part of the characteristic matrix. The application of this method to the stability analysis of Hopf bifurcation points is quite efficient. The use of a determining system for Hopf bifurcation points allows to trace branches of Hopf points via continuation.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 932494
zbMATH Keywords: stability
zbMATH Keywords: Hopf bifurcation points
zbMATH Keywords: systems of nonlinear delay differential equations
zbMATH Keywords: characteristic matrix
reviewed by: Pavol Chocholatý
describes a project that uses: LOCBIF
MaRDI profile type: Publication
full work available at URL: 0377-0427(96)00008-8
OpenAlex ID: W2095172584
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Wikidata QID: Q127991554
description: scientific article; zbMATH DE number 932494