ANALYSIS OF THE EQUILIBRIUM PROPERTIES OF A CONTINUOUS NEURAL NETWORK MADE OF EXCITATORY AND INHIBITORY NEURONS

A mathematical approach to studying the properties of maps between a signal space and two neural fields, one of excitatory and the other of inhibitory neurons, is presented. It is based on a modified version of Amari's field-theoretic approach. Under certain simplifying assumptions, it is shown that the sizes of the amplifications of signals in the inhibitory neural field are inversely related to the sizes of the receptive fields of the excitatory and inhibitory neurons in the signal space. Other results concerning the relationships between the sizes of the amplifications of signals and the receptive fields of neurons, and the probabilities of occurrence of signals, are obtained and discussed.