Effects of correlation among stored patterns on associative dynamics of chaotic neural network

Abstract

We numerically investigate the effects of correlation among stored patterns on the associative dynamics in a chaotic neural network model. In the model, there are two kinds of parameters: one is a measure of the Hopfield like behavior of the retrieval process and another controls the chaotic behavior. The parameter dependence of the associative dynamics is also examined. The following results are found. (i) Two dimensional parameter space is divided into two kinds of associative states by a distinct boundary. One is the retrieval state of the association such as the Hopfield like retrieval state, and another is the wandering state of the associative dynamics where the network retrieves stored patterns and their reverse patterns. (ii) The area of the wandering state becomes larger as the degree of correlation becomes larger. (iii) As the degree of correlation becomes larger, both the recall ratio of correlated patterns and the transition frequency between correlated patterns becomes larger in the wandering state. (iv) The whole region of the wandering state in the parameter space is not necessarily chaotic from the view point of the Lyapunov dimension, but most of the region of the wandering state is chaotic.