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1. A digital computer has been programmed to simulate a neuronal network consisting of eighty cells with the following characteristics:

(a) All cells in the network had a set random probability of discharge when not affected by other cells. The probability of discharge was chosen as one system parameter (PD).

(b) Subsequent to the firing of any neurone in the network, a certain number of other neurones underwent a change in their probability of discharge, consisting of an inhibitory period followed by a period of increased excitability. The changes of excitability mimic the changes of the membrane potential recorded for spontaneously rhythmically active cells in the animal thalamus.

2. Starting the network, a typical transient response appeared, consisting of a burst-like activity. The initial activity was followed, first by random fluctuations of the number of active cells, later by periods of spontaneous rhythmic activity that had several characteristics in common with the type of spontaneous activity seen in the animal thalamus.

3. The parameters which affected the rhythmic activity of the network most strongly were the degree of the post-inhibitory increase of the probability of discharge and the degree of distribution of the inhibition to neighbouring cells.

4. The results are compatible with the inhibitory phasing theory advanced by Andersen & Sears (1964) to explain the occurrence of spontaneous rhythmic activity in the animal thalamus. However, before sufficient experimental knowledge is available, it is difficult to establish whether the rhythmic activity in the network is of the same type as that of the animal thalamus.

5. A closer study of the parameters governing the behaviour of the simulated network has given indications of some parameters to be more closely investigated in future animal experiments.