Models of genetic control by repression with time delays and spatial effects
 J. M. Mahaffy,
 C. V. Pao
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Two models for cellular control by repression are developed in this paper. The models use standard theory from compartmental analysis and biochemical kinetics. The models include time delays to account for the processes of transcription and translation and diffusion to account for spatial effects in the cell. This consideration leads to a coupled system of reactiondiffusion equations with time delays. An analysis of the steadystate problem is given. Some results on the existence and uniqueness of a global solution and stability of the steadystate problem are summarized, and numerical simulations showing stability and periodicity are presented. A Hopf bifurcation result and a theorem on asymptotic stability are given for the limiting case of the models without diffusion.
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 Title
 Models of genetic control by repression with time delays and spatial effects
 Journal

Journal of Mathematical Biology
Volume 20, Issue 1 , pp 3957
 Cover Date
 19840801
 DOI
 10.1007/BF00275860
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Genetic control models
 reaction
 diffusion equations with delays
 Authors

 J. M. Mahaffy ^{(1)}
 C. V. Pao ^{(1)}
 Author Affiliations

 1. Department of Mathematics, North Carolina State University, 27650, Raleigh, NC, USA