Chaotic Brownian network

A system of many Brownian particles interacting via the chaotic force is proposed as a new model of neural network, which is called the chaotic Brownian network. The network is applied to the associative memory problem. The coupling constants are determined by the Hebb rule. It is shown that some neuron pairs, which are specified by the stored patterns, exhibit the synchronized motions with the same sign or with the opposite sign. The relation between the synchronized motion and the chaotic wandering motion is discussed. The network is shown to retrieve the stored patterns or the reverse ones systematically and very quickly. It is shown that the network can store and retrieve the number of patterns comparable to the number of neurons.