A MATHEMATICAL STUDY OF SELF- ORGANIZING NERVE SYSTEMS

Abstract

We treat very simple nerve net models for the sake of tractability, such that we obtain explicitly the behaviours of the models. This enables us to know how the behaviours of the models depend on the values of the system parameters and to know the possible information processing manners of neuron nets. The study is devoted in two parts first part treats the general equation of neural learning in a unified manner. Thus, perceprons learning, correlation learning for associative memory, automatic formation of signal or feature detectors etc, are studied in this common frame. The second part treats dynamics of neural excitation. Dynamics of neuron pools, of neural fields, and of a completion model are analysed. By combining the result of first and second parts, we can analyze self organizing neural systems: We analyze a model of formation of signal or feature detectors, and a model of topographic organization of nerve fields.