Abstract: The bifurcation mechanisms of the Borghans-Dupont model of calcium oscillation were investigated．By applying the centre manifold and bifurcation theory,a theoretical analysis of bifurcation in this model was first performed．The results not only exhibite the Hopf bifurcation but also show that the supercritical Hopf bifurcation and the subcritical Hopf bifurcation play a great role in the calcium oscillations．Our computer simulations,including the bifurcation diagram of fixed points,the bifurcation diagram of the system in two dimensional parameter space and time series,have been plotted in order to illustrate the correctness of the theoretical and dynamical analysis.

Key words: Calcium oscillation,Hopf bifurcation,Centre manifold,Equilibrium,Stability,Limit cycle