Attractors of random dynamical systems over p-adic numbers and a model of ‘noisy’ cognitive processes

Abstract

We propose a mathematical model of a cognitive system which can be used to simulate features of the real thinking process. In this model states of a cognitive system (‘ideas’) are coded by canonical expansions of p-adic numbers. The p-adic metric on the space of cognitive states describes the ability to form associations. The course within a cognitive system is a feedback process described by a p-adic dynamical system whose attractors form the possible results of the thinking process. We study how a cognitive system works in the presence of noise. Our main result is that a large class of p-adic random dynamical systems exists which has only deterministic attractors. In this class noise cannot disturb the results of cognitive processes.