Extensive research has demonstrated that astrocytes actively participate in the regulation of synaptic communication. To examine the dynamic behavior of the model, a neuron-astrocyte model has been solved, and a bifurcation analysis has been performed. This paper uses the equilibrium point, stability theory, and the center manifold theorem to theoretically investigate the dynamical analysis of Ca2+ oscillations in the cytosol. The connections at tripartite synapses between the cells have been modeled using IP3 and 2-AG. A mathematical model is used to depict the overall framework of bifurcation and induced Ca2+ dynamics. The differences in the presence and disappearance of Ca2+ oscillations are partially explained by two subcritical Hopf bifurcation points, according to the results. Communication between the cells occurs through the oscillations of Ca2+ concentration. Furthermore, numerical simulations are conducted to confirm the efficacy of the suggested approach. Thus, our findings imply that neuron-astrocyte crosstalk plays a fundamental role in generating a variety of neuronal activities, thereby improving the brain's capacity for information processing.
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