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Šimon, Peter; Hild, Elizabeth; Farkas, Henrik

doi:10.1023/a:1010943118331

Journal of Mathematical Chemistry

2001

DOI: 10.1023/a:1010943118331

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Peter Šimon

Elizabeth Hild

Henrik Farkas

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Cited by 6 publications

References 13 publications

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

Nagy

2008

Applied Mathematical Modelling

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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.

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

Nagy

2008

Applied Mathematical Modelling

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Analysis of the biological clock of Neurospora

Nagy¹

2009

Journal of Computational and Applied Mathematics

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a b s t r a c t A dynamical system describing the circadian fluctuation of a protein (FRQ) in Neurospora cells is investigated from the bifurcation point of view. The possible phase portraits and local bifurcations are studied. The saddle-node and Hopf-bifurcation curves are determined in the plane of two parameters using the parametric representation method. The number and the stability of the stationary points are determined. Using center manifold approximation we determine the Bautin-bifurcation point numerically.

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Numerical and analytical study of bifurcations in a model of electrochemical reactions in fuel cells

CsöRg

Šimon

2013

Computers & Mathematics with Applications

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Untitled

Cited by 6 publications

References 13 publications

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

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

Analysis of the biological clock of Neurospora

Numerical and analytical study of bifurcations in a model of electrochemical reactions in fuel cells

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