Numerical Simulations and Bifurcation of Ca2+ Oscillatory Behaviour in the Connection of Neurons and Astrocytes

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.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.