ISSN:
1432-1416
Keywords:
Genetic control models
;
reaction
;
diffusion equations with delays
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract 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 steady-state problem is given. Some results on the existence and uniqueness of a global solution and stability of the steady-state 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00275860
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