Some comments on activation and inhibition

A system of rate equations gives rise to a corresponding pattern of activation and inhibition between the state variables. We consider the converse question: to what extent does the specification of a pattern of activation and inhibition between interacting quantities determine the rate equations? Among other things, it is shown that in order to determine a closed set of rate equations, a set of integrability conditions among the interactions must be satisfied; hence there is a sense in which an activation-inhibition pattern is more general than systems of rate equations. Questions of the structural stability of activation-inhibition patterns, and of the time-scales determined by dynamical interactions, are briefly discussed. A comparison is made between the properties of such activation-inhibition patterns and those of neural networks, or more general modular automata.