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.
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.
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
\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}
\elib{https://elibrary.ru/item.asp?id=41271060}
Linking options:
https://www.mathnet.ru/eng/vsgtu1678
https://www.mathnet.ru/eng/vsgtu/v223/i2/p378
This publication is cited in the following 2 articles:
Roman Parovik, Zafar Rakhmonov, Rakhim Zunnunov, A. Dmitriev, G. Vodinchar, Z. Rakhmonov, “Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov”, EPJ Web Conf., 254 (2021), 02014
Roman Parovik, Zafar Rakhmonov, Rakhimzhon Zunnunov, A. Dmitriev, G. Vodinchar, N. Salikhov, Z. Rakhmonov, “Modeling of fracture concentration by Sel'kov fractional dynamic system”, E3S Web Conf., 196 (2020), 02018
Citation in format AMSBIB
Contact us: