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

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

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 dia...

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Bibliographic Details
Main Author: R. I. Parovik
Format: Article
Language:English
Published: Samara State Technical University 2019-06-01
Series:Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
Subjects:
duffing-type fractal oscillator
gram–schmidt orthogonalization
wolf's algorithm
maximum exponent spectrum
fractional derivative gerasimov–caputo
bifurcation diagrams
phase trajectories
Online Access:http://mi.mathnet.ru/eng/vsgtu1678
Description
Summary: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.
ISSN:1991-8615
2310-7081

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