Abstract
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. © 1997 Elsevier Science Ltd.
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