Modeling and Quantitative-Qualitative Analysis of Two-Dimensional Generators of Chaotic Signals Based on Modular Arithmetic

Abstract

In this article, by the combined application of the programs E&F Chaos, Past, Fractan, Eviews Student Version Lite, mathematical, numerical and computer modeling of some of the well-known two-dimensional generators of chaotic signals based on modular arithmetic presented in [4] was carried out, and the properties of the obtained chaotic signals were evaluated using nonlinear dynamics methods (time and spectral diagrams, BDS-statistics, Hurst exponent). As a result of the conducted research, it was found that the time and spectral diagrams obtained for the studied two-dimensional generators of chaotic signal based on modular arithmetic have a complex noise-like appearance similar to white noise. The resulting range of BDS-statistics values corresponds to white noise at a certain interval, and persistent processes (black noise) at a certain interval. The resulting range of values of the Hurst exponent is also close to white noise. The results obtained show that two-dimensional generators of chaotic signals based on modular arithmetic can relate to white noise and have more pronounced chaotic properties than classical generators of chaotic signals, on the basis of which they are created. The results obtained complement and expand the knowledge about two-dimensional generators of chaotic signals based on modular arithmetic and open up broad prospects for their use in various practical applications.