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

A. Yu. Jalnine ; S. P. Kuznetsov

Russian journal of nonlinear dynamics, Tome 13 (2017) no. 2, pp. 257-275.

Résumé

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.

Détail

Keywords: autonomous dynamical system, mechanical rotators, quasi-periodic oscillations, strange nonchaotic attractor
Mots-clés : chaos.

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