Analytical study on the associative memory problem in coupled Hopfield neural networks

In coupled Hopfield neural networks, in which different patterns are stored in each network, the associative memor problem is investigated. It has been shown numerically by several authors that in coupled two chaotic neural netowrks, where different patterns are stored, one network can retrieve that pattern stored in other network. In the Hopfield theory a stored pattern corresponds always to an attractor in the dynamical sense. The retrieval of the pattern stored in other network means that the state of Netowrk A approaches no the attractor of Netowrk A but the attractor of Netowrk B by coupling Network A with B. In this paper, we study this problem in an analytic approach. It is shown that the final pattern of the each network is classified into 4 types according to the initial condition and the connection constant. By introducing the energy function of the total system the problem is also investigated from a viewpoint of energy. We propose the system, in which many Hopfield networks are connected, and its application is discussed.