The Stability of the Generalized Hopfield Networks in Randomly Asynchronous Mode

We present a study on the stability of the generalized Hopfield network in randomly asynchronous mode. First, the stability is investigated from the state space of the network. We introduce a concept of hole and define two kinds of stability in randomly asynchronous mode. By mathematical inductive method, we have proved that a generalized Hopfield network with non negative weights is strictly stable, that is, the network evolves to a simple hole-stable state with probability one when it starts at any initial state. For the general case, we made the simulation experiments on the networks with the number of neurons from 5 to 10. The empirical results have shown that almost any generalized Hopfield network with simple holes is strictly stable. Copyright 1997 Elsevier Science Ltd.