Cellular-Automata-Like Simulations of Dynamic Neural Fields

Abstract

In modelling neuronal phenomena one can generally choose two different methods (Levine, 1991): One way is to setup a network of discrete model neurons and all their interconnection weights, which is usually done in the so-called PDP approach (Rumelhart and McClelland, 1986; McClelland and Rumelhart, 1986). The main interest lies on the learning capabilities of the established network, i. e. on the correct adaptations of the connection weights, in order to generate the correct output for a given input. Another approach to neuronal modelling is using continuous networks (so-called fields) with special attention to the spatio-temporal activities of the network. The number of neurons is unlimited in these models, and the connections between the neurons are handled in a general way (e. g. statistically) without having individually changing weights. Therefore, instead of being interested in the learning mechanisms of the network one investigates the various dynamics of the fields. It is a convenient way to describe the evolution equations of the field by integro-differential equations (IDEs).