Linear Analysis of an Integro-Differential Delay Equation Model

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...

Full description

Saved in:
Bibliographic Details
Published in:International journal of differential equations 2018-01, Vol.2018 (2018), p.1-6
Main Author: Verdugo, Anael
Format: Article
Language:English
Subjects:
Biological models (mathematics)
Biology
Boundary value problems
Computational mathematics
Cytoplasm
Delay
Delay equations
Differential equations
Economic models
Gene expression
Linear analysis
Mathematical research
Negative feedback
Ordinary differential equations
Partial differential equations
Proteins
Steady state
Time lag
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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.
ISSN:1687-9643
1687-9651
DOI:10.1155/2018/5035402