International Journal of Differential Equations

Linear Analysis of an Integro-Differential Delay Equation Model

Anael Verdugo

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Abstract

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.

Article information

Source
Int. J. Differ. Equ., Volume 2018 (2018), Article ID 5035402, 6 pages.

Dates
Received: 2 December 2017
Accepted: 14 March 2018
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1528855325

Digital Object Identifier
doi:10.1155/2018/5035402

Mathematical Reviews number (MathSciNet)
MR3801852

Zentralblatt MATH identifier
06915955

Citation

Verdugo, Anael. Linear Analysis of an Integro-Differential Delay Equation Model. Int. J. Differ. Equ. 2018 (2018), Article ID 5035402, 6 pages. doi:10.1155/2018/5035402. https://projecteuclid.org/euclid.ijde/1528855325


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