Interacting Brownian particles as a model of neural network

A model of neural network is proposed, in which the dynamics of the internal state of neurons is based on the Brownian motion with the chaotic force, and the bifurcation parameter of the chaotic force is modulated by the position of the Brownian particles. This model is applied to the associative memory problem. The parameter dependence of the dynamics is studied. It is shown that the model can retrieve all embedded patterns and reverse patterns successively. It is found that all neurons exhibit synchronized behavior while a pattern is retrieved.