Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback

doi:10.1007/s10440-010-9584-4

	Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback
	Qiao, YuanHua 1; Jia, Erze 1; Miao, Jun 2
	2011
发表期刊	ACTA APPLICANDAE MATHEMATICAE
ISSN	0167-8019
卷号	113 期号:1 页码:57-73
摘要	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.
关键词	Delay differential equations Circadian rhythm model Stability Hopf bifurcation
DOI	10.1007/s10440-010-9584-4
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of China[60702031] ; Natural Science Foundation of China[60970087] ; Beijing Natural Science Foundation[4102013]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000285203800005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/13103
专题	中国科学院计算技术研究所期刊论文_英文
通讯作者	Qiao, YuanHua
作者单位	1.Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China 2.Chinese Acad Sci, Key Lab Intelligent Informat Proc, Inst Comp Technol, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Qiao, YuanHua,Jia, Erze,Miao, Jun. Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback[J]. ACTA APPLICANDAE MATHEMATICAE,2011,113(1):57-73.
APA	Qiao, YuanHua,Jia, Erze,&Miao, Jun.(2011).Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback.ACTA APPLICANDAE MATHEMATICAE,113(1),57-73.
MLA	Qiao, YuanHua,et al."Stability and Hopf Bifurcation of a Type of Protein Synthesis System with Time Delay and Negative Feedback".ACTA APPLICANDAE MATHEMATICAE 113.1(2011):57-73.