Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 49. no. 4. P. 36 – 49. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2024-49-4-36-49
Research Article
Full text in Russian
MSC 34A30

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On a Ssystem of Coupled Linear Oscillators with Fractional Friction and Non-Constant Coefficients for Describing Geoacoustic Emission

D. F. Sergienko¹²^{\ast}, R. I. Parovik²

¹Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya str., 4, Russia
²Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, 684034, Paratunka village, Mirnaya str., 7, Russia

Abstract. The paper proposes a generalization of the previously obtained mathematical model of geoacoustic emission, according to which the model takes into account the effects of heredity in dissipative terms. The model is a system of two coupled linear oscillators with non-constant coefficients and with fractional derivatives of Gerasimov-Caputo orders, which describe viscous friction (fractional friction). The mathematical model is studied numerically using a non-local explicit finite-difference scheme of the first order of accuracy, which was implemented in the Maple 2022 computer symbolic mathematics environment. In this computer environment, the modeling results were visualized: oscillograms and phase trajectories were constructed for different values of the model parameters. The interpretation of the modeling results is given. It is shown that fractional friction can affect the process of interaction of geoacoustic emission sources.

Key words: geoacoustic emission, Gerasimov-Caputo fractional derivative, model, oscillograms, phase trajectory, Maple 2022.

Received: 21.10.2024; Revised: 12.11.2024; Accepted: 22.11.2024; First online: 27.11.2024

For citation. Sergienko D. F., Parovik R. I. On a system of coupled linear oscillators with fractional friction and nonconstant coefficients for describing geoacoustic emission. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 49: 4, 36-49. EDN: MKTALS. https://doi.org/10.26117/2079-6641-2024-49-4-36-49.

Funding. The work was funded by Russian Science Foundation [grant number 22-11-00064 «Modeling dynamic processes in geospheres taking into account hereditarity»]. https://rscf.ru/project/22-11-00064/

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.

^{\ast}Correspondence: E-mail: darya@ikir.ru

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

© Sergienko D. F., Parovik R. I., 2024

© Institute of Cosmophysical Research and Radio Wave Propagation, 2024 (original layout, design, compilation)

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Sergienko Darya Faritovna – aspirant of the Department of Mathematics and Computer Science, Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, Russia; programmer of the Laboratory of Acoustic Research, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, S. Paratunka, Russia ORCID 0009-0008-6512-4537.

Parovik Roman Ivanovich – Doctor of Physico-Mathematical Sciences, Professor, Leading Researcher at the Laboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, S. Paratunka, Russia ORCID 0000-0002-1576-1860.

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