Characteristics of Random Nets of Analog Neuron-Like Elements

The dynamic behavior of randomly connected analog neuron-like elements that process pulse-frequency modulated signals is investigated from the macroscopic point of view. By extracting two statistical parameters, the macroscopic state equations are derived in terms of these parameters under some hypotheses on the stochastics of microscopic states. It is shown that a random net of statistically symmetric structure is monostable or bistable, and the stability criteria are explicitly given. Random nets consisting of many different classes of elements are also analyzed. Special attention is paid to nets of randomly connected excitatory and inhibitory elements. It is shown that a stable oscillation exists in such a net-in contrast with the fact that no stable oscillations exist in a net of statistically symmetric structure even if negative as well as positive synaptic weights are permitted at a time. The results are checked by computer-simulated experiments.