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Current theories about the dynamics of neural networks with nonlinear characteristics and parameterized by set of parameters are mostly based on approximations in one way or another. In this paper we first introduce a rigorous approach which allows us to check in which parameter region a given saturated state is an attractor of the dynamics: a saturated state w=(wi, i=1,...,N)?{-1,1}N is an attractor of the dynamics if and only if there is a local field gap between neurons in J+(w)={i, wi=1} and J-(w)={i, wi=-1}. Then we apply the result to analyze several models in neural networks. In particular in the Hopfield model we calculate the capacity and give an exact relation between the capacity and the threshold.

A novel approach for analyzing dynamics in neural networks with saturated characteristics