Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/225405

Title

The stability and Hopf bifurcation analysis of a gene expression model

Author(s)

Zhang, Tonghua;  Song, Yongli;  Zang, Hong

Abstract

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.

Publication type

Journal article

Research centre

Swinburne University of Technology. Faculty of Engineering and Industrial Sciences

Source

Journal of Mathematical Analysis and Applications, Vol. 395, no. 1 (Nov 2012), pp. 103-113

Publication year

2012

FOR Code(s)

0101 Pure Mathematics;  0102 Applied Mathematics;  0906 Electrical and Electronic Engineering

Keyword(s)

Delay differential equation;  Gene expression model;  Hopf bifurcation;  Normal form

Publisher

Elsevier

ISSN

0022-247X

Publisher URL

http://dx.doi.org/10.1016/j.jmaa.2012.05.032

Copyright

Copyright © 2012 Elsevier Ltd. All rights reserved.

Additional information

The authors acknowledge support from the National Natural Science Foundation of China (11001212 and 11101318), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Fundamental Research Funds for the Central Universities and the Program for New Century Excellent Talents in University (NCET-11-0385).

Peer reviewed