A numerical verification method for a periodic solution of a delay differential equation
type: Item
instance of: scholarly article
title: A numerical verification method for a periodic solution of a delay differential equation
zbMATH Open document ID: 1202.65086
author: Teruya Minamoto
author: Mitsuhiro T. Nakao
published in: Journal of Computational and Applied Mathematics
publication date: 2010-10-11T00:00:00Z
review text: The authors develop a new numerical verification method for a system of delay differential equations: \[ \begin{aligned} \dot x(t) & = -y(t)-z(t), \dot y(t)=x(t)+(0.2)y(t)+u(t)\\ \dot z(t) & = 0.2 + z(t)(x(t)-5.7), u(t)=k(y(t-\tau)-y(t)). \end{aligned} \] By using this system of equations corresponding to the original Rössler system, they derive sufficient conditions for the existence of the solution. They describe the verification procedure in detail with conditions and provide a numerical example.
Mathematics Subject Classification ID: 65L03
zbMATH DE Number: 5798205
zbMATH Keywords: delay differential equation
zbMATH Keywords: numerical computation with guaranteed accuracy
zbMATH Keywords: delayed feedback control
zbMATH Keywords: Rössler system
reviewed by: R. S. Dahiya
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: j.cam.2010.07.018
OpenAlex ID: W1992657189
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Wikidata QID: Q115359845
DOI: 10.1016/J.CAM.2010.07.018
description: scientific article; zbMATH DE number 5798205