On the Stability of a Periodic Solution of a Differential Delay Equation

1975 ◽  
Vol 6 (2) ◽  
pp. 268-282 ◽  
Author(s):  
James L. Kaplan ◽  
James A. Yorke
Keyword(s):  
Periodic Solution ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
The Stability

scholarly journals Response of an oscillatory differential delay equation to a single stimulus

2016 ◽  
Vol 74 (5) ◽  
pp. 1139-1196 ◽  
Author(s):  
Michael C. Mackey ◽  
Marta Tyran-Kamińska ◽  
Hans-Otto Walther
Keyword(s):  
Single Stimulus ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
Differential Delay

Differential-Delay Equation Model of Gene Expression: A Continuum Approach

2008 ◽  
Author(s):  
Anael Verdugo ◽  
Richard H. Rand
Keyword(s):  
Analytical Study ◽  
Equation Model ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
Differential Integral Equation ◽  
Gene Regulatory ◽  
The Stability ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Nonlinear Delay

This paper presents an analytical study of the stability of the steady state solutions of a gene regulatory network with time delay. The system is modeled as a continuous network and takes the form of a nonlinear delay differential-integral equation coupled to an ordinary differential equation. Two examples are given in which the critical delay causing instability is computed.

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