Ca2+ oscillations play an important role in various cell types. Thus, understanding the dynamical mechanisms underlying astrocytic Ca2+ oscillations is of great importance. The main purpose of this article was to investigate dynamical behaviors and bifurcation mechanisms associated with astrocytic Ca2+ oscillations, including stability of equilibrium and classification of different dynamical activities including regular and chaotic Ca2+ oscillations. Computation results show that part of the reason for the appearance and disappearance of spontaneous astrocytic Ca2+ 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 Ca2+ oscillations in conjunction with the adjacent neuronal input that may help correlate the connection of both the glia and neuron.
The complexity of ECG signal based on multifractal theories and its nonlinear dynamical mechanism
