A method of analysis of the models of neural nets

Abstract

Taking into account Caianiello's work of 1961 a model of a neuron quite similar to his is proposed and studied. For this model, where a temporal summation and a period of refractoriness are assumed, a mathematical approach and a simulation on computer were realized. Particular types of nets were used, namely: nets with topological structures, and fully random nets. The difference between the two types is that the first type has a two-dimensional square structure and depends on the rules of the formation of connection between the neurons, while the second type is realized by means of the probability distribution function governing the formation of the structure of the net.

These types of neural nets are analysed by means of a method which permits to obtain various parameters which characterize their behaviour in time and space in terms of the trajectory of the system. Many experiments are also reported; the statistical analyses, made on them, show the great importance and influence of refractoriness on the behaviour of neural networks.

In the last part of the work an interesting case is reported, in which the reaction of the net to a disturbance shows that a kind of adaptation takes place, although the structure of the net stays unchanged.