Synchronization and stable phase-locking in a network of neurons with memory

We consider a network of three identical neurons whose dynamics is governed by the Hopfield's model with delay to account for the finite switching spe ed of amplifiers (neurons). We show that in a certain region of the space o f (alpha, beta), where alpha and beta are the normalized parameters measuri ng, respectively, the synaptic strength of self-connection and neighbourhoo d-interaction, each solution of the network is convergent to the set of syn chronous states in the phase space, and this synchronization is independent of the size of the delay. We also obtain a surface; as the graph of a cont inuous function of tau = tau(alpha, beta) (the normalized delay) in some re gion of (alpha, beta), where Hopf bifurcation of periodic solutions takes p lace. We describe a continuous curve on such a surface where the system und ergoes mode-interaction and we describe the change of patterns from stable synchronous periodic solutions to the coexistence of two stable phase-locke d oscillations and several unstable mirror-reflecting waves and standing wa ves. (C) 1999 Elsevier Science Ltd. All rights reserved.