Vestnik КRAUNC. Fiz.-Mat. nauki. 2023. vol. 44. no. 3. P. 67-85. ISSN 2079-6641

MATHEMATICAL MODELING

https://doi.org/10.26117/2079-6641-2023-44-3-67-85

Research Article

Full text in Russian

MSC 34A08, 34A34

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Implementation of the Modified Test 0-1 Algorithm for the Analysis of Chaotic Modes of the Fractional Duffing Oscillator

R. I. Parovik¹²^\ast

¹Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, st. Pogranichnaya, 4, Russia
²National University of Uzbekistan named after Mirzo Ulugbek, 100174, Tashkent, st. Universitetskaya, 4, Uzbekistan

Abstract. The work carried out a study of chaotic and regular modes of a fractional Duffing oscillator using the Test 0-1 algorithm. The fractional Duffing oscillator is described by a nonlinear differential equation with the Riemann-Liouville derivative of a fractional variable order. Using an explicit numerical finitedifference scheme, a numerical solution to the model was obtained, which is fed to the input of the Test 0-1 algorithm after the thinning procedure – identifying local extrema. Next, using the Matlab package, the Test 0-1 algorithm is implemented and the simulation results are visualized. Bifurcation diagrams are constructed for the correlation coefficient, taking into account the values of the orders of the fractional derivative, and oscillograms and phase trajectories are constructed. It is shown that the Test 0-1 algorithm works correctly with the appropriate selection of the sampling step.

Key words: Test 0-1, model, Duffing oscillator, Riemann-Liouville fractional derivative, standard deviation, correlation, bifurcation diagram

Received: 01.09.2023; Revised: 01.10.2023; Accepted: 05.10.2023; First online: 02.11.2023

For citation. Parovik R. I. Implementation of the modified Test 0-1 algorithm for the analysis of chaotic modes of the fractional Duffing oscillator. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 44: 3, 67-85. EDN: AREVER. https://doi.org/10.26117/2079-6641-2023-44-3-67-85.

Funding. The research was carried out within the framework of the grant of the President of the Russian Federation MD-758.2022.1.1 on the topic “Development of mathematical models of fractional dynamics in order to study oscillatory processes and processes with saturation”

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing
the final version of the article in print. The final version of the manuscript was approved by all authors.

^\astCorrespondence: E-mail: romanparovik@gmail.com

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Parovik R. I., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)

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Information about author

Parovik Roman Ivanovich – D. Sci. (Phys. & Math.), Associate Professor, Leading researcher, laboratory of modeling physical processes Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Head of the International Integrative Research Laboratory of Extreme Phenomena of Kamchatka, Kamchatka State University named after Vitus Bering, Petropavlovsk-Kamchatsky, Russia, ORCID 0000-0002-1576-1860.

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