A NEURAL NETWORK FOR STORING INDIVIDUAL PATTERNS IN LIMIT-CYCLES

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. We find that the model with cycles performs better than a similarly diluted version of the Hopfield model. The performance of the fully connected model is studied by numerical simulations. We find a behaviour qualitatively similar to that of the dilute model. The model with cycles is found to perform better than the Hopfield model as a pattern classifier if the memory loading level and the degree of corruption of the input patterns are high.