Hybrid neural nets with poisson and gaussian connectivities

Abstract

The dynamic behavior of neural nets with different patterns of interneuronal synaptic connectivity is investigated. Our method is based on probabilistic neural nets for the net structure and dynamics. Each net is divided into several different subsystems, which are characterized by different distribution laws for the number of connections that the neurons make. We start from the binomial distribution, which, under appropriate conditions, reduces to the Poisson and Gaussian distributions. The overall net now acquires a hybrid character. The expression for the neural activity is generalized to include this effect, and new expressions are derived, based on the isolated single-net equations. The dynamics of nets with sustained external inputs is also studied. The results obtained by this approach also show multiple stability and multiple hysteresis effects, as in the case of single nets. The differences between pure Poisson, Gaussian, and hybrid nets are explained in terms of the structural properties of the model. As expected, the hybrid case falls in between the two other distributions. Finally, we performed Monte Carlo computer calculations for the hybrid nets. For the range of parameters examined we find very good agreement with the developed formalism