Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

摘要

We study associative memory based on temporal coding in which successfulretrieval is realized as an entrainment in a network of simple phaseoscillators with distributed natural frequencies under the influence of whitenoise. The memory patterns are assumed to be given by uniformly distributedrandom numbers on $[0,2\pi)$ so that the patterns encode the phase differencesof the oscillators. To derive the macroscopic order parameter equations for thenetwork with an extensive number of stored patterns, we introduce the effectivetransfer function by assuming the fixed-point equation of the form of the TAPequation, which describes the time-averaged output as a function of theeffective time-averaged local field. Properties of the networks associated withsynchronization phenomena for a discrete symmetric natural frequencydistribution with three frequency components are studied based on the orderparameter equations, and are shown to be in good agreement with the results ofnumerical simulations. Two types of retrieval states are found to occur withrespect to the degree of synchronization, when the size of the width of thenatural frequency distribution is changed.