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Richness of chaotic dynamics in nonholonomic models of a celtic stone

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Abstract

We study the regular and chaotic dynamics of two nonholonomic models of a Celtic stone. We show that in the first model (the so-called BM-model of a Celtic stone) the chaotic dynamics arises sharply, during a subcritical period doubling bifurcation of a stable limit cycle, and undergoes certain stages of development under the change of a parameter including the appearance of spiral (Shilnikov-like) strange attractors and mixed dynamics. For the second model, we prove (numerically) the existence of Lorenz-like attractors (we call them discrete Lorenz attractors) and trace both scenarios of development and break-down of these attractors.

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Authors and Affiliations

  1. Research Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod State University, ul. Ul’yanova 10, Nizhny Novgorod, 603005, Russia

    Alexander S. Gonchenko, Sergey V. Gonchenko & Alexey O. Kazakov

  2. Institute of Computer Science, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    Alexey O. Kazakov

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  1. Alexander S. Gonchenko
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  2. Sergey V. Gonchenko
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  3. Alexey O. Kazakov
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Correspondence to Alexander S. Gonchenko.

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Gonchenko, A.S., Gonchenko, S.V. & Kazakov, A.O. Richness of chaotic dynamics in nonholonomic models of a celtic stone. Regul. Chaot. Dyn. 18, 521–538 (2013). https://doi.org/10.1134/S1560354713050055

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