Fractal approach to the identification of complex systems
DOI:
https://doi.org/10.15407/dopovidi2017.06.046Keywords:
complex system, fractal, Lorentz carrousel, mathematical model, nuclear reactor, self-similarity areaAbstract
A possibility of applying the fractal models for the identification of complex systems is considered. An algorithm for determining the area of self-similarity of the object under consideration is presented. The algorithm allows one to reduce the probability of the object malfunctioning.
Downloads
References
Cherepanov, V. V., Prylutskyy, Yu. I., Senenko, A. I., Marchenko, A. A. & Naumovets, A. G. (2014). Nanoscale systems and nanomaterials research in Ukraine. Editorial board: A.G. Naumovets (glav. red.). Kiev: Academperiodika, pp. 15-18 (in Russian).
Naumovets, A. G. & Bespalov, S. A. (2014). Nano-sized systems: structure, properties, technologies (International scientific conference NANSYS-2013). Visn. Nac. acad. nauk Ukraine, No. 2, pp. 67-69 (in Russian).
Bol'shakov, V., Volchuk, V. & Dubrov, Yu. (2016). Fractals and properties of materials. Saarbrücken: Palmarium Academic Publishing.
Bulat, A. F. & Dyrda, V. I. (2005). Fractals in geomechanics. Kiev: Naukova Dumka (in Russian).
Grinchenko, V. T., Matsypura, V. T., Snarskiy, A. A. (2005). Introduction to nonlinear dynamics. Chaos and Fractals. Kiev: Naukova Dumka (in Russian).
Bol'shakov, V. I., Volchuk, V. N. & Dubrov, Yu. I. (2008). Peculiarities of applications of the multifractal formalism to materials science. Dopov. Nac. acad. nauk Ukraine, No. 11, pp. 99-107 (in Russian).
Bol'shakov, V. I. & Volchuk, V. N. (2008). Materials science aspects of applications of the wavelet-multifractal approach to the evaluation of a structure and properties of low-carbon steel. Metallofizika i Noveishie Tek hnologii, 33, No. 3, pp. 347-360 (in Russian).
Lorenz, E.N.I. (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20, pp. 130-141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
Bol'shakov, V. I. & Dubrov, Yu. I. (2016). On a possibility to identify computationally irreducible systems. Visn. Nac. acad. nauk Ukraine, No. 3, pp. 76-80 (in Ukrainian), https://doi.org/10.15407/visn2016.03.076
Bol'shakov Vad. I., Bol'shakov V. I., Volchuk V. N. & Dubrov Yu. I. (2014). A partial compensation of the incompleteness of a formal axiomatics at the identification of a metal structure. Visn. Nac. acad. nauk Ukraine, No. 12, pp. 45-48 (in Ukrainian).
Beer, S. (1959). Cybernetics and Management. London: English Universities Press.
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Matematica und verwandter Systeme. Monatshefte für Mathematik und Physik, 38, pp. 173-198 (in Germany). https://doi.org/10.1007/BF01700692
-INSAG-7 in. LL. CO. INSAG-7. The Chernobyl Accident: Updating of INSAG-1. International Atomic Energy Agency, Vienna, 1992.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
