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This article is cited in 7 scientific papers (total in 7 papers)
Autonomous Strange Nonchaotic Oscillations in a System of Mechanical Rotators
Alexey Yu. Jalnineab, Sergey P. Kuznetsovab a Saratov Branch of Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS,
ul. Zelenaya 38, Saratov, 410019 Russia
b Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
Abstract:
We investigate strange nonchaotic self-oscillations in a dissipative system consisting
of three mechanical rotators driven by a constant torque applied to one of them. The
external driving is nonoscillatory; the incommensurable frequency ratio in vibrational-rotational
dynamics arises due to an irrational ratio of diameters of the rotating elements involved. It is
shown that, when losing stable equilibrium, the system can demonstrate two- or three-frequency
quasi-periodic, chaotic and strange nonchaotic self-oscillations. The conclusions of the work
are confirmed by numerical calculations of Lyapunov exponents, fractal dimensions, spectral
analysis, and by special methods of detection of a strange nonchaotic attractor (SNA): phase
sensitivity and analysis using rational approximation for the frequency ratio. In particular,
SNA possesses a zero value of the largest Lyapunov exponent (and negative values of the other
exponents), a capacitive dimension close to 2 and a singular continuous power spectrum. In
general, the results of this work shed a new light on the occurrence of strange nonchaotic
dynamics.
Keywords:
autonomous dynamical system, mechanical rotators, quasi-periodic oscillations, strange nonchaotic attractor, chaos.
Received: 31.03.2017 Accepted: 18.04.2017
Citation:
Alexey Yu. Jalnine, Sergey P. Kuznetsov, “Autonomous Strange Nonchaotic Oscillations in a System of Mechanical Rotators”, Regul. Chaotic Dyn., 22:3 (2017), 210–225
Linking options:
https://www.mathnet.ru/eng/rcd252 https://www.mathnet.ru/eng/rcd/v22/i3/p210
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Abstract page: | 185 | References: | 39 |
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