Stability and Hopf bifurcation in a model of gene expression with distributed time delays

被引：26
|
作者：
Song, Yongli [1 ]
Han, Yanyan [1 ]
Zhang, Tonghua [2 ]
机构：
[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China
[2] Swinburne Univ Technol, Dept Math, Melbourne, Vic 3122, Australia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 243卷
关键词：
Gene expression; Distributed time delay; Stability; Hopf bifurcation; OSCILLATORY EXPRESSION; HES1;
D O I：
10.1016/j.amc.2014.05.122
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the effect of distributed time delays on dynamics of a mathematical model of gene expression. Both the weak and strong delay kernels are discussed. Sufficient conditions for the local stability of the unique equilibrium are obtained. Taking the average delay as a bifurcation parameter, we investigate the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the method of multiple time scales. Finally, numerical simulation is carried out to illustrate our theoretical results. It shows both subcritical and supercritical Hopf bifurcations can happen. (C) 2014 Elsevier Inc. All rights reserved.
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页码：398 / 412
页数：15
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