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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 2, Pages 378–393 (Mi vsgtu1678)  

Mathematical Modeling, Numerical Methods and Software Complexes

The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator

R. I. Parovikab

a Institute of Cosmophysical Researches and Radio Wave Propagation, Far East Division, Russian Academy of Sciences, Paratunka, Kamchatkiy kray, 684034, Russian Federation
b Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatskiy, 683032, Russian Federation

Abstract: In this paper, we study the chaotic regimes of the fractional Duffing oscillator. To do this, using the Wolf algorithm with Gram–Schmidt orthogonalization, we calculated the spectra of maximum Lyapunov exponents depending on the values of the control parameters, on the basis of which bifurcation diagrams were constructed. Bifurcation diagrams made it possible to determine areas in which a chaotic oscillatory regime exists. Phase trajectories were also constructed, which confirmed the research results.

Keywords: Duffing-type fractal oscillator, Gram–Schmidt orthogonalization, Wolf's algorithm, maximum exponent spectrum, fractional derivative Gerasimov–Caputo, bifurcation diagrams, phase trajectories

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-1152.2018.1
This work was supported by the grant of the President of the Russian Federation for state support of scholarly research by young scholars no. MK-1152.2018.1.


DOI: https://doi.org/10.14498/vsgtu1678

Full text: PDF file (1260 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.938
MSC: 26A33, 34A08, 37N30, 74H60
Received: February 25, 2019
Revised: June 3, 2019
Accepted: June 10, 2019
First online: June 28, 2019

Citation: R. I. Parovik, “The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 378–393

Citation in format AMSBIB
\Bibitem{Par19}
\by R.~I.~Parovik
\paper The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 2
\pages 378--393
\mathnet{http://mi.mathnet.ru/vsgtu1678}
\crossref{https://doi.org/10.14498/vsgtu1678}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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