Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback |
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| Authors: | YuanHua Qiao Erze Jia Jun Miao |
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| Affiliation: | 1. College of Applied Science, Beijing University of Technology, 100124, Beijing, China
2. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, 100190, Beijing, China
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| Abstract: | This paper studied the stability and Hopf bifurcation of a type of protein synthesis system with time delay and negative feedback. Firstly, it is proved theoretically that the time delay, nonlinearity in the protein production and the cooperativity in the negative feedback are key factors to generate circadian oscillation; Taking time delay as a parameter, we obtained the critical value of the time delay that Hopf bifurcation generates. Secondly, based on the center manifold and normal form theorem, we derived the formulas for determining the stability of bifurcating periodic solutions and the supercritical or subcritical Hopf bifurcation. Finally, the matlab program is used to simulate the results. |
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