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Nelin. Dinam., 2017, Volume 13, Number 2, Pages 257–275 (Mi nd564)  

Translated papers

Autonomous strange non-chaotic oscillations in a system of mechanical rotators

A. Yu. Jalninea, S. P. Kuznetsovb

a Saratov Branch of Kotelnikovs 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

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
Russian Foundation for Basic Research 16-02-00135


DOI: https://doi.org/10.20537/nd1702008

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English version:
Regular and Chaotic Dynamics, 2017, 22:3, 210–225

UDC: 517.9, 531.36
MSC: 34C15, 34C28, 34C46, 37C55, 37C70, 37D45, 70K43
Received: 31.03.2017
Accepted:18.04.2017

Citation: A. Yu. Jalnine, S. P. Kuznetsov, “Autonomous strange non-chaotic oscillations in a system of mechanical rotators”, Nelin. Dinam., 13:2 (2017), 257–275; Regular and Chaotic Dynamics, 22:3 (2017), 210–225

Citation in format AMSBIB
\Bibitem{JalKuz17}
\by A.~Yu.~Jalnine, S.~P.~Kuznetsov
\paper Autonomous strange non-chaotic oscillations in a system of mechanical rotators
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 2
\pages 257--275
\mathnet{http://mi.mathnet.ru/nd564}
\crossref{https://doi.org/10.20537/nd1702008}
\elib{http://elibrary.ru/item.asp?id=29443381}
\transl
\jour Regular and Chaotic Dynamics
\yr 2017
\vol 22
\issue 3
\pages 210--225
\crossref{https://doi.org/10.1134/S1560354717030029}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020173459}


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