  A mathematical model of a spiking neuron network accompanied by astrocytes is
considered. The network is composed of excitatory and inhibitory neurons with
synaptic connections supplied by a memristor-based model of plasticity. Another
mechanism for changing the synaptic connections involves astrocytic regulations
using the concept of tripartite synapses. In the absence of memristor-based
plasticity, the connections between these neurons drive the network dynamics
into a burst mode, as observed in many experimental neurobiological studies
when investigating living networks in neuronal cultures. The memristive
plasticity implementing synaptic plasticity in inhibitory synapses results in a
shift in network dynamics towards an asynchronous mode. Next,it is found that
accounting for astrocytic regulation in glutamatergic excitatory synapses
enable the restoration of 'normal' burst dynamics. The conditions and
parameters of such astrocytic regulation's impact on burst dynamics
established.
