Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model
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.