Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model

Nagy, Bálint (2008) Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model. Applied Mathematical Modelling, 32 (8). pp. 1587-1598. ISSN 0307-904X

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Abstract

Two dynamical systems describing the circadian fluctuation of two proteins (PER and TIM) in cells are compared. A simplified model with two variables has already been investigated. Detailed study of the possible bifurcation has been carried out. Periodic solutions of the differential equations with 24-h period have been obtained numerically. Here the general, more realistic model having three variables is investigated. The possible phase portraits and local bifurcations are studied in detail. The saddle-node and Hopf-bifurcation curves are determined in the plane of two parameters by using the parametric representation method. Using these curves the number and the type of the stationary points can be determined. The relation of the two bifurcation curves and the Takens–Bogdanov bifurcation points are also studied. The bifurcation curves are compared to those obtained for the simplified two-variable system.

Item Type:	Article
Uncontrolled Keywords:	Parametric representation method; Hopf-bifurcation; Saddle-node bifurcation; Takens–Bogdanov bifurcation; Circadian rhythm model
Divisions:	Informatika Intézet > Matematikai és Számítástudományi Tanszék
Depositing User:	Gergely Beregi
Date Deposited:	23 Jun 2021 09:13
Last Modified:	23 Jun 2021 09:13
URI:	http://publication.repo.uniduna.hu/id/eprint/803
MTMT:	1973929

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