p-Adic discrete dynamical systems and collective behaviour of information states in cognitive models

Abstract

We develop a model of functioning of complex information systems (in particular, cognitive systems) in that information states are coded by p-adic integers. An information state evolves by iterations of a discrete p-adic dynamical system. The p-adic utrametric on the space of information states (p-adic homogeneous tree) describes the ability of an information system to operate with associations. The main attention is paid to the collective dynamics of families of associations.