Neural networks with connections, formed with a help of multi-ring activity sets

Neural networks, based on multi-ring activity sets are considered. It is shown, that such sets are useful for synthesis of neural networks with a predetermined sequence of activity pattern. An algorithm for a NN interconnection matrix, giving robust decision to the problem is proposed and studied at length. Some results of a further analysis are presented for the NN of the Hebb-Hopfield (HH) type, i.e. for a NN whose interconnection matrix is the Hebb matrix of Hopfield. It is shown, that for the case, when the multi-ring activity set is a basic set for the HH network, minima of its Hopfield energy are at the bottom of deep ditches, corresponding to the basic set of network activity states for the HH NN. When neuron threshold fatigue is introduced, depending on its recent activity state, the network activity becomes cyclic, moving with a constant rate, depending on λ in one of the possible directions in the ring, depending on the initial conditions. The results are most interesting, when more than one full ring (say, two or more) are being used as a basic set for an HH matrix. The pairs of full rings with random, in relation to each other, enumerations (N=256) are being tested. Properties of excitation states in such networks in relation to each full ring of the HH network basic set are the same as properties of the single full ring based HH network activity. The phenomena described present a novel robust type of neural network behavior. They have a high probability of being encountered in living neural systems