Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells
The Borghans-Dupont model of calcium oscillations based on both the calcium-induced calcium release and calcium-activated inositol trisphosphate concentration degradation is considered. Dynamical effect of the stimulation level on the calcium oscillation behavior is studied. The qualitative theory of differential equations is used to explain the mechanism of these oscillations. We investigate the existence, types, stability and bifurcations of the equilibria by applying the centre manifold theorem, stability theory and bifurcation theory and prove that oscillations are due to supercritical Hopf bifurcation. Finally, we perform numerical simulations, including time courses, phase portraits and bifurcation diagram, to validate the correctness and the effectiveness of our theoretical analysis. These results may be instructive for understanding the role of the stimulation level played in complex dynamics in this model.
Chunliang Zhang and Paul P. Lin
Y. Zhou et al., "Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells", Applied Mechanics and Materials, Vols. 226-228, pp. 521-525, 2012