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Hopf bifurcation analysis in a model of oscillatory gene expression with delay

Published online by Cambridge University Press:  08 July 2009

Junjie Wei  and
Chunbo Yu
Junjie Wei
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China (weijj@hit.edu.cn)
Chunbo Yu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China
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Abstract

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The dynamics of a gene expression model with time delay are investigated. The investigation confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. An explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions has been derived by using the theory of the centre manifold and the normal forms method. The global existence of periodic solutions has been established using a global Hopf bifurcation result by Wu and a Bendixson criterion for higher-dimensional ordinary differential equations due to Li and Muldowney.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 879 - 895
Copyright
Copyright © Royal Society of Edinburgh 2009