Hopf bifurcation analysis for a model of genetic regulatory system with delay

This paper deals with a mathematical model that describe a genetic regulatory system. The model has a delay which affects the dynamics of the system. We investigate the stability switches when the delay varies, and show that Hopf bifurcations may occur within certain range of the model parameters. B...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 356; no. 2; pp. 464 - 476
Main Authors Wan, Aying, Zou, Xingfu
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.08.2009
Elsevier
Subjects
Delay
Exact sciences and technology
Genetic regulatory system
Global analysis, analysis on manifolds
Hopf bifurcation
Mathematical analysis
Mathematics
Periodic solution
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Hopf bifurcation
Periodic solution
Genetic regulatory system
Delay
Manifold
Mathematical analysis
Normal form
Numerical simulation
Delay system
Mathematical model
Application
Numerical stability
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Summary:This paper deals with a mathematical model that describe a genetic regulatory system. The model has a delay which affects the dynamics of the system. We investigate the stability switches when the delay varies, and show that Hopf bifurcations may occur within certain range of the model parameters. By combining the normal form method with the center manifold theorem, we are able to determine the direction of the bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical simulations are carried out to support the analytic results.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.03.037