International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2018 (2018), Article ID 5035402, 6 pages.
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 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 delay differential equations (DDEs) coupled to 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 becomes large.
Int. J. Differ. Equ., Volume 2018 (2018), Article ID 5035402, 6 pages.
Received: 2 December 2017
Accepted: 14 March 2018
First available in Project Euclid: 13 June 2018
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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