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Regular and Chaotic Dynamics

, Volume 22, Issue 3, pp 210–225 | Cite as

Autonomous strange nonchaotic oscillations in a system of mechanical rotators

  • Alexey Yu. Jalnine
  • Sergey P. Kuznetsov
Article
  • 54 Downloads

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 

MSC2010 numbers

34C15 34C28 34C46 37C55 37C70 37D45 70K43 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Saratov Branch of Kotel’nikov’s Institute of Radio-Engineering and Electronics of RASSaratovRussia
  2. 2.Udmurt State UniversityIzhevskRussia

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