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Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

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Abstract

Dynamical equations are formulated and a numerical study is provided for selfoscillatory model systems based on the triple linkage hinge mechanism of Thurston–Weeks–Hunt–MacKay. We consider systems with a holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.

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Authors and Affiliations

  1. Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Sergey P. Kuznetsov

  2. Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia

    Sergey P. Kuznetsov

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  1. Sergey P. Kuznetsov
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Kuznetsov, S.P. Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories. Regul. Chaot. Dyn. 20, 649–666 (2015). https://doi.org/10.1134/S1560354715060027

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  • DOI: https://doi.org/10.1134/S1560354715060027

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