Topological methods in measurement and research of nonlinear dynamical systems

doi:10.26565/2222-5617-2018-29-04

Yurii Kurskoy Kharkov National University of Radioelectronics, Nauki Av., 14, Kharkov, 61166, Ukraine https://orcid.org/0000-0002-1333-2931
Yurii Machekhin Kharkov National University of Radioelectronics, Nauki Av., 14, Kharkov, 61166, Ukraine
A. S. Gnatenko Kharkov National University of Radioelectronics, Nauki Av., 14, Kharkov, 61166, Ukraine

DOI: https://doi.org/10.26565/2222-5617-2018-29-04

Keywords: nonlinear dynamical system, topology, chaos, Shannon entropy, fractal dimension

Abstract

The authors substantiate the need to create a special theory of measurement and analysis of measurement results for nonlinear dynamical systems. The theory should be based on the principles of the open systems theory, dynamic chaos theory and synergetics theory. The authors analyzed the main topological methods and tools for studying of nonlinear dynamic systems. The main characteristics of nonlinear dynamical systems (interval values of dynamic variables, strong dependence on initial conditions and noise, complex, often chaotic dynamics, evolution) were systematized. It was proposed the next topological tools for analysis of measurement results in nonlinear dynamical systems: measurement portrait, Shennon entropy, fractal dimension, forecasting time.

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