Computation and stability analysis of Hopf Bifurcation in biophysical system model of cells

Dynamics of the Shen-Larter calcium oscillation model is investigated based on the theory of the center manifold and bifurcation, including the classification and stability of equilibrium. The existence of two subcritical Hopf bifurcations is derived in this case. More precisely, it is shown that the subcritical Hopf bi-furcations play a great role in the study of this calcium oscillation model. In addition, numerical simulations are provided to verify our theoretical analysis and to display new phenomena. Based on the theoretical analysis results and the numerical results, an effective mechanism explaining the Shen-Larter calcium oscillation model is obtained.