Dynamical analysis of spontaneous Ca²⁺ oscillations in astrocytes

In this work, we focus on a nonlinear dynamical model proposed by Lavrentovich et al. to compute and simulate spontaneous Ca²⁺ oscillations evoked by calcium ion efflux in astrocytes. Selected parameters are chosen, with observation of periodic and chaotic Ca²⁺ oscillations in cytosol. The stability analysis of equilibrium is conducted using the center manifold theorem to investigate the dynamics underlying spontaneous Ca²⁺ oscillations in astrocytes. The results indicate that the Hopf bifurcation represents the dynamical changes in stability of spontaneous Ca²⁺ oscillations. In addition, numerical simulations are performed to further assess the validity of the aforementioned analysis.