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This article is cited in 2 scientific papers (total in 2 papers)
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
(published under the terms of the Creative Commons Attribution 4.0 International License)
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.
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
Linking options:
https://www.mathnet.ru/eng/vsgtu1678 https://www.mathnet.ru/eng/vsgtu/v223/i2/p378
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