BEHAVIOR OF FIXED POINT CONGRUENT PERIODIC TRAJECTORIES OF NONLINEAR MAPS IN DYNAMICAL SYSTEMS THEORY

Abstract

This paper considers problems that arise during number sequence generation based on nonlinear dynamical systems. Complex systems can depend on many parameters analysis and examination of
one-dimensional maps was per-formed since these maps are dynamical systems. Dependence of iterative
fixed points for nonlinear maps on the properties of functions and function domain numbers was investigated. Several approaches to randomness evaluation and, accordingly, methods for estimating the degree of
randomness of a particular sequence were considered. The properties and internal structure of sequences
obtained on the basis of nonlinear maps were also examined in accordance to their influence on the degree
of randomness.