Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model

Hong Kun Zuo; Quan Bao Ji; Yi Zhou

doi:10.4028/www.scientific.net/AMM.226-228.510

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Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model
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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 226-228Hopf Bifurcation and Numerical Simulation in a...

Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model

Abstract:

Calcium oscillations play a very important role in providing the intracellular signaling, and many mathematical models have been proposed to describe calcium oscillations. The Shen-Larter model presented here is based on calcium-induced calcium release (CICR) and the inositol trisphosphate cross-coupling (ICC). Nonlinear dynamics of this model is investigated by using the centre manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with different parameter values. The results show that the appearance and disappearance of calcium oscillations are due to subcritical Hopf bifurcation of equilibria. The numerical simulations are performed in order to illustrate the correctness of our theoretical analysis, including the bifurcation diagram of fixed points, the phase diagram of the system in two dimensional space and time series.

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Periodical:

Applied Mechanics and Materials (Volumes 226-228)

Pages:

510-515

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.226-228.510

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Online since:

November 2012

Authors:

Hong Kun Zuo, Quan Bao Ji, Yi Zhou

Keywords:

Calcium Oscillation, Centre Manifold, Equilibrium, Hopf Bifurcation

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References

[1] U. Kummer, L.F. Olsen, C.J. Dixon, A.K. Green, E. Bornberg-Bauer and G. Baier: Biophys vol. 79 (2000), p.95.

Google Scholar

[2] A.Goldbeter: Biochemical oscillations and cellular rhythms (Cambridge University press, England 1996).

Google Scholar

[3] N.M. Woods, K.S.R. Kuthbertson and P.H. Cobbold: Cells Calcium, vol. 8 (1987), p.79.

Google Scholar

[4] P. Shen and R. Larter : Biophys Chem, vol. 66 (1997), p.25.

Google Scholar

[5] J.A.M Borghans, G. Dupont, A. Goldbeter: Biophys Chem, vol. 66 (1997), p.25.

Google Scholar

[6] C.K. Yan, S.Q. Liu: Acta Biophsical Sinica, vol. 21 (2005), No.5, p.339 (In Chinese).

Google Scholar

[7] L.J. Zhang, J. Wang, Y. Chang: Journal of Beijing University of Chemical Technology (Natural Science), vol. 35 (2008) No. 3, p.104–107. (In Chinese)

Google Scholar

[8] L.L. Zhou, X.D. Li, Y. Chang: Journal of Beijing University of Chemical Technology (Natural Science), vol. 37 (2010) No. 3, p.134–139. (In Chinese)

Google Scholar

[9] M. Perc, M. Marrhl: Solutions and Fractals, vol. 18 (2003), p.759.

Google Scholar

[10] S. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos. (Springer, Germany 1990).

Google Scholar

[11] Z J Jing, Y. Chang, B.L. Guo: Chaos Solitions and Fractals, vol. 21 (2004), No.3, p.701. (In Chinese).

Google Scholar