The dynamics of logical decisions: a neural network approach

In the context of modular neural networks we show that it is possible to define logical gates as matrix associative memories. This matrix formalism is able to represent logical decisions as dynamical dialogues among neural modules. If the interactions among these modules are mapped onto a subspace of positive identifications they give rise to dynamical systems on Rn. In the presence of uncertainties (fuzzy logical variables), some decisions can produce cognitive versions of the classical Gause and Lotka–Volterra models, in others, exhibit chaotic behavior. We investigate decisions in the presence of many alternative choices. In these situations, the emergence of instability is strongly dependent on several factors, among them, dimension, connectivity and initial conditions.