Topological Methods in Nonlinear Analysis

Notes on circadian rhythm

Claudio Saccon and Robert E.L. Turner

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Abstract

We discuss a class of models arising in the study of circadian rhythm and the properties of the matrix equations providing the bifurcation points for a wide parameter class. In particular, we prove that the five dimensional system studied in the cited work of Gonze, Halloy, and Goldbeter can have only a simple Hopf bifurcation.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 41, Number 2 (2013), 387-400.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461245484

Mathematical Reviews number (MathSciNet)
MR3114314

Zentralblatt MATH identifier
1291.34084

Citation

Saccon, Claudio; Turner, Robert E.L. Notes on circadian rhythm. Topol. Methods Nonlinear Anal. 41 (2013), no. 2, 387--400. https://projecteuclid.org/euclid.tmna/1461245484


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References

  • S.-N. Chow and J.K. Hale (1982, Methods of Bifurcation Theory, Grundl. Math. Wiss., Springer, Berlin) \ref\key 2
    Mathematical Reviews (MathSciNet): MR660633
  • L. Edelstein-Keshet (2005, Mathematical Models in Biology, SIAM Classics in Applied Mathematics, 46 , SIAM) \ref\key 3
    Mathematical Reviews (MathSciNet): MR2131632
  • A. Goldbeter and O. Pourquié (2008, Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt, and FGF signaling pathways , J. Theor. Biology, 252 ), 574–585 \ref\key 4
    Mathematical Reviews (MathSciNet): MR2961112
    Digital Object Identifier: doi:10.1016/j.jtbi.2008.01.006
  • A. Goldbeter, C. Gerard and J.-C. Leloup (2010, Biologie des Systems et Rythmes Cellulaires , Medecine/Science, 26 ), 49–56 \ref\key 5
  • D. Gonze, J. Halloy and A. Goldbeter (2004, Emergence of coherent oscillations in stochastic mModels for circadian rhythms , Physica A: Statistical Mechanics and its Applications, 342 ), 221–233 \ref\key 6
  • T. Kato (1995, Perturbation Theory for Linear Operators, Springer, Berlin)
    Mathematical Reviews (MathSciNet): MR1335452

Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies

Topological Methods in Nonlinear Analysis

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