Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 13, Issue 2, Pages 235-242Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2006.05.001
Keywords
delay; DDE; Hopf bifurcation; gene transcription
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We analyze a model of gene transcription and protein synthesis which has been previously presented in the biological literature. The model takes the form of an ODE (ordinary differential equation) coupled to a DDE (delay differential equation), the state variables being concentrations of messenger RNA and protein. Linear analysis gives a critical time delay beyond which a periodic motion is born in a Hopf bifurcation. Lindstedt's method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. A parameter study shows that the Hopf bifurcation may not occur if the rates of degradation are too large. (c) 2006 Elsevier B.V. All rights reserved.
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