Bifurcation and Numerical Simulations of Ca2+ Oscillatory Behavior in Astrocytes

In this paper the dynamical analysis of Ca2+ oscillations in astrocytes is theoretically investigated by the center manifold theorem and the stability theory of equilibrium point. The global structure of bifurcation and evoked Ca2+ dynamics are presented in a human astrocyte model from a mathematical perspective. Results show that the difference in appearance and disappearance of Ca2+ oscillations is partly due to two subcritical Hopf bifurcation points. In addition, the numerical simulations are performed to further verify the effectiveness of the proposed method.