An application of the saturated attractor analysis to three typical models

Abstract

The saturated attractor analysis, an approach proposed first in [FP] for a comprehensive study of the dynamics of the Linsker model and then successfully applied to the dynamic link model[FT1], is further developed here. By a unified approach to the Hopfield model, the Linsker model and the dynamic link model, three typical models in the field of the neural networks, we show a way to choose the parameters of these dynamics in order to obtain any chosen saturated attractor which is general enough in most applications. We generalize our previous results for the Linsker model and the dynamic link model with the clipping function to the case of the sigmoid like function. Our results allow us for the first time to understand the underlying mechanism among these models and thus to furnish a useful guidance in the further possible applications.