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We propose two-compartment model of calcium dynamics in astrocyte network, basing on Ullah model [1]. In order to count the specific features of different parts of astrocyte network we mark out three types of modelling space: astrocyte soma with thick branches, thin branches, and extracellular space. We have developed two variants of equation set which are different in relative contribution of specific ionic currents. We suppose that activation of astrocyte calcium dynamics is mediated by the extracellular space, specifically, via diffusion of synaptic glutamate released due to the neuronal activity, which we describe as some random signal incorporating noise effects. We have performed a number of simulation runs at different parameter sets for individual astrocyte and multi-cell network. One of simulation examples within the computational multi-cell template is given in Figure 1. The global wave emerging in one of the points passes through the wide region of astrocyte network. The formation of the wave has a high degree of regularity and periodicity. There are also local regimes where excitation waves damp passing through a small number of cells.