Linear analysis of an integro-differential delay equation model
type: Item
instance of: scholarly article
title: Linear analysis of an integro-differential delay equation model
zbMATH Open document ID: 1487.34141
DOI: 10.1155/2018/5035402
author: Anael Verdugo
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: This paper presents a computational study of the stability of the steady state solutions of a biological model with negative feedback and time delay. The motivation behind the construction of our system comes from biological gene networks, and the model takes the form of an integro-delay differential equation (IDDE) coupled to a partial differential equation. Linear analysis shows the existence of a critical delay where the stable steady state becomes unstable. Closed form expressions for the critical delay and associated frequency are found and confirmed by approximating the IDDE model with a system of \(N\) delay differential equations (DDEs) coupled to \(N\) ordinary differential equations. An example is then given that shows how the critical delay for the DDE system approaches the results for the IDDE model as \(N\) becomes large.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92C37
zbMATH DE Number: 6915955
zbMATH Keywords: stability of steady state solutions
zbMATH Keywords: biological model with negative feedback and time delay
Wikidata QID: Q115243957
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5035402
OpenAlex ID: W2799747180
cites work: Hopf bifurcation in a DDE model of gene expression
cites work: Qualitative simulation of genetic regulatory networks using piecewise-linear models
cites work: Structure of regulatory networks and diversity of gene expression patterns
cites work: Periodicity in piecewise-linear switching networks with delay
cites work: Center manifold analysis of a DDE model of gene expression
description: scientific article; zbMATH DE number 6915955