A simple model of a neuronal circuit based on a stochastic discrete-time difference equation is described. The model assumes loosely connected clusters of densely connected neurons within each cluster, and a circuit topology is produced by connecting the clusters in sequence. The action of the glia is simulated by two parameters referring to its trophic action in restoring neuronal energy levels after firing and to its scavenging action at the synaptic level affecting the probability that an impulse is transmitted. It is shown that only glial trophic support within a limited range allows ordinate cyclic functioning of the circuit. It is also shown that changes in local action at the synapse determine changes in the frequency of the cycling. This kind of model paves the way to a quantitative description of changes in neurodegenerative diseases, so as to potentially predict the evolution of quality of life in these conditions.