The stability and Hopf bifurcation analysis of a gene expression model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Zhang, Tonghua¹  Song, Yongli²  Zang, Hong³ 

[1] Swinburne Univ Technol, Fac Engn & Ind Sci, Hawthorn, Vic 3122, Australia

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[3] Wuhan Inst Technol, Sch Comp Sci & Engn, Wuhan, Peoples R China

关键词: Delay differential equation;    Gene expression model;    Normal form;    Hopf bifurcation;   

DOI  :  10.1016/j.jmaa.2012.05.032

来源: Elsevier

【 摘 要 】

In this paper, we investigate a model for gene expression, unlike the models mathematically analyzed previously we have both transcriptional and translational time delays. The stability and Hopf bifurcation of the equilibrium point are investigated. Different to previous papers, a multiple time scale (MTS) technique is employed to calculate the normal form on the center manifold of system of delay differential equations, which is much easier to implement in practice than the conventional method, center manifold reduction. Our results show that when time delay is small the equilibrium is stable, when it is at its critical value Hopf bifurcation happens and while for very large value of time delay the oscillation sustains, which has been confirmed by the published data and proved mathematically by using the global continuity of the Hopf bifurcation in this paper. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free