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...

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Autores principales:	Parovik Roman, Rakhmonov Zafar, Zunnunov Rakhim
Formato:	article
Lenguaje:	EN
Publicado:	EDP Sciences 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/9a68b5af9372432187bb93db89819a9a
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spelling	oai:doaj.org-article:9a68b5af9372432187bb93db89819a9a2021-11-12T11:44:52ZStudy of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov2100-014X10.1051/epjconf/202125402014https://doaj.org/article/9a68b5af9372432187bb93db89819a9a2021-01-01T00:00:00Zhttps://www.epj-conferences.org/articles/epjconf/pdf/2021/08/epjconf_strpep2021_02014.pdfhttps://doaj.org/toc/2100-014XThe 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.Parovik RomanRakhmonov ZafarZunnunov RakhimEDP SciencesarticlePhysicsQC1-999ENEPJ Web of Conferences, Vol 254, p 02014 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Parovik Roman Rakhmonov Zafar Zunnunov Rakhim Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov
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.
format	article
author	Parovik Roman Rakhmonov Zafar Zunnunov Rakhim
author_facet	Parovik Roman Rakhmonov Zafar Zunnunov Rakhim
author_sort	Parovik Roman
title	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_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_sort	study of chaotic and regular modes of the fractional dynamic system of selkov
publisher	EDP Sciences
publishDate	2021
url	https://doaj.org/article/9a68b5af9372432187bb93db89819a9a
work_keys_str_mv	AT parovikroman studyofchaoticandregularmodesofthefractionaldynamicsystemofselkov AT rakhmonovzafar studyofchaoticandregularmodesofthefractionaldynamicsystemofselkov AT zunnunovrakhim studyofchaoticandregularmodesofthefractionaldynamicsystemofselkov
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Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov

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