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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICAL MODELING OF DYNAMIC SYSTEMS
Calculation the maximum Lyapunov exponent for the oscillatory system of Duffing with a degree memory
V. A. Kima, R. I. Parovikba a Vitus Bering Kamchatka State University, 683032, Kamchatskiy kray, 4, Pogranichnaya Str., Russia Petropavlovsk-Kamchatsky, Russia
b Institute of Cosmophysical Researches and Radio Wave Propagation, Far East Division, Russian Academy of Sciences
Abstract:
In the study of nonlinear systems, one of the important problems is the determination of the type of oscillations-periodic, quasi-periodic, random, chaotic. It is especially difficult to distinguish between quasi-periodic oscillations from chaotic and random oscillations, since quasi-periodic oscillations often have a very complex shape, visually weakly distinguishable from «random». A feature of chaotic oscillations is their high sensitivity to small changes in the initial conditions. Therefore, one of the most reliable ways of detecting chaos is to determine the rate of run-off of trajectories, which is estimated using the Lyapunov exponent spectrum. Using the construction of the spectrum of Max Lyapunov exponents, depending on the values of the control parameters, chaotic regimes of the Duffing fractal oscillator with variable power memory were found, and its phase trajectories.
Keywords:
spectrum of maximum Lyapunov exponents, Duffing fractal oscillator, phase trajectories, limit cycle, chaotic attractor.
Received: 10.06.2018
Citation:
V. A. Kim, R. I. Parovik, “Calculation the maximum Lyapunov exponent for the oscillatory system of Duffing with a degree memory”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 98–105
Linking options:
https://www.mathnet.ru/eng/vkam260 https://www.mathnet.ru/eng/vkam/y2018/i3/p98
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