MEMORY RECALL BY QUASI-FIXED-POINT ATTRACTORS IN OSCILLATOR NEURAL NETWORKS

It is shown that approximate fixed-point attractors rather than synchr onized oscillations can be employed by a wide class of neural networks of oscillators to achieve an associative memory recall. This computat ional ability of oscillator neural networks is ensured by the fact tha t reduced dynamic equations for phase variables in general involve two terms that can be respectively responsible for the emergence of synch ronization and cessation of oscillations. Thus the cessation occurs in memory retrieval if the corresponding term dominates in the dynamic e quations. A bottomless feature of the energy function for such a syste m makes the retrieval states quasi-fixed points, which admit continual rotating motion to a small portion of oscillators, when an extensive number of memory patterns are embedded. An approximate theory based on the self-consistent signal-to-noise analysis enables one to study the equilibrium properties of the neural network of phase variables with the quasi-fixed-point attractors. As far as the memory retrieval by th e quasi-fixed points is concerned, the equilibrium properties includin g the storage capacity of oscillator neural networks are proved to be similar to those of the Hopfield type neural networks.