The linear theory of neuron networks: The dynamic problem

Abstract

The development of a general theory of neuron-networks is here extended to cases of non-steady state activity. Conditions for stability and neutrality of an equilibrium point are set up, and the possible functions representing the variation of excitation over time are enumerated. The inverse network problem is considered—which is, given a preassigned pattern of activity over time, to construct when possible a neuron-network having this pattern. Finally, a canonical form for neuron networks is derived, in the sense of a network of a certain special topological structure which is equivalent in activity characteristics to any given network.