The purpose of this work is to study the role of mechanisms of astrocytic regulation of synaptic transmission in the processes of synchronization formation in signaling of neural networks by mathematical modeling methods.

Methods. The paper presents a model of a small neuron-astrocyte ensemble. The HodgkinHuxley model is used as a model of the membrane potential dynamics of a neuron. The case of an ordered topology of connections ("all-to-all") in a neural network is considered. The astrocyte network is modeled as a network of diffusion-coupled calcium oscillators with an ordered topology (in which the matrix of connections is structured in a certain way, interaction with the nearest neighbors). A biophysical model of calcium dynamics is used as
an astrocyte model. The effect of astrocytes on neurons is taken into account as a slow modulation of synaptic connections weights in the neural network, proportional to calcium signals in nearby astrocytes. In other words, at the network level, the possibility of adaptive restructuring of oscillatory wave patterns due to astrocyte-induced regulation of synaptic transmission is being studied. The synchronization of neuronal activity is estimated by calculating the coherence of the neural network signaling.

Results. The influence of astrocytes on the dynamics of the neural network consists in the excitation of time-correlated patterns of neural activity caused by an astrocytedependent increase in synaptic interaction between neurons on the time scales of astrocytic dynamics. It has been shown that synchronized calcium signaling of the astrocytic network leads to coordinated burst (bundle) activity of the neural network, which occurs against the background of uncorrelated spontaneous impulse activity induced by external noise stimulation. The influence of specific biophysical mechanisms of astrocytic modulation of synaptic transmission on the dynamic properties of local synchronization structures in neural ensembles has been investigated. The characteristics of the coordinated bundle activity of a neural network are studied depending on the properties of external noise stimulation, the strength of astrocytic regulation of synaptic transmission, as well as the degree of neurons influence on astrocytes.