Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov
The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2021-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://www.epj-conferences.org/articles/epjconf/pdf/2021/08/epjconf_strpep2021_02014.pdf |
| _version_ | 1818824169321660416 |
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| author | Parovik Roman Rakhmonov Zafar Zunnunov Rakhim |
| author_facet | Parovik Roman Rakhmonov Zafar Zunnunov Rakhim |
| author_sort | Parovik Roman |
| collection | DOAJ |
| description | The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration. |
| first_indexed | 2024-12-18T23:51:36Z |
| format | Article |
| id | doaj.art-9a68b5af9372432187bb93db89819a9a |
| institution | Directory Open Access Journal |
| issn | 2100-014X |
| language | English |
| last_indexed | 2024-12-18T23:51:36Z |
| publishDate | 2021-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | EPJ Web of Conferences |
| spelling | doaj.art-9a68b5af9372432187bb93db89819a9a2022-12-21T20:46:55ZengEDP SciencesEPJ Web of Conferences2100-014X2021-01-012540201410.1051/epjconf/202125402014epjconf_strpep2021_02014Study of Chaotic and Regular Modes of the Fractional Dynamic System of SelkovParovik Roman0Rakhmonov Zafar1Zunnunov Rakhim2Institute of Cosmophysical Research and Radio Wave Propagation FEB RASNational University of Uzbekistan named after Mirzo UlugbekInstitute of Mechanics and Seismic Resistance of Structures named after M.T. UrazbayevaThe paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration.https://www.epj-conferences.org/articles/epjconf/pdf/2021/08/epjconf_strpep2021_02014.pdf |
| spellingShingle | Parovik Roman Rakhmonov Zafar Zunnunov Rakhim Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov EPJ Web of Conferences |
| title | Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov |
| title_full | Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov |
| title_fullStr | Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov |
| title_full_unstemmed | Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov |
| title_short | Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov |
| title_sort | study of chaotic and regular modes of the fractional dynamic system of selkov |
| url | https://www.epj-conferences.org/articles/epjconf/pdf/2021/08/epjconf_strpep2021_02014.pdf |
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