Geodesic
The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 378-393

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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. 
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     author = {R. I. Parovik},
     title = {The existence of chaotic regimes of the fractional analogue of the {Duffing-type} oscillator},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {378--393},
     publisher = {mathdoc},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2019_23_2_a9/}
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R. I. Parovik. The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 378-393. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_2_a9/