Mathematical modeling of formation processes of sequences with fractal elements of periodical chaotic dynamical system trajectories

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 performed since these maps are dymanical 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.