A neural network for storing individual patterns in limit cycles

Abstract

A neural network model in which individual memories are stored in limit cycles is studied analytically and numerically. In this model there are two kinds of interactions: a Hopfield-like term that tends to stabilize the system in a memorized state and a second term with a time delay that acts to induce transitions between a memorized state and its complement state. For a proper choice of the values of the parameters, this model exhibits limit cycle behaviour in which the overlap with a target pattern oscillates in time. An asymmetrically diluted version of the model is studied analytically in the limit of extreme dilution.