Stability analysis of regular and chaotic \(\mathrm{Ca^{2+}}\) oscillations in astrocytes (Q2004207)

Summary: \(\mathrm{Ca^{2+}}\) oscillations play an important role in various cell types. Thus, understanding the dynamical mechanisms underlying astrocytic \(\mathrm{Ca^{2+}}\) oscillations is of great importance. The main purpose of this article was to investigate dynamical behaviors and bifurcation mechanisms associated with astrocytic \(\mathrm{Ca^{2+}}\) oscillations, including stability of equilibrium and classification of different dynamical activities including regular and chaotic \(\mathrm{Ca^{2+}}\) oscillations. Computation results show that part of the reason for the appearance and disappearance of spontaneous astrocytic \(\mathrm{Ca^{2+}}\) oscillations is that they embody the subcritical Hopf and the supercritical Hopf bifurcation points. In more details, we theoretically analyze the stability of the equilibrium points and illustrate the regular and chaotic spontaneous calcium firing activities in the astrocytes model, which are qualitatively similar to actual biological experiment. Then, we investigate the effectiveness and the accuracy of our nonlinear dynamical mechanism analysis via computer simulations. These results suggest the important role of spontaneous \(\mathrm{Ca^{2+}}\) oscillations in conjunction with the adjacent neuronal input that may help correlate the connection of both the glia and neuron.