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.
This work was supported by the RFBR grants №11-01-00001, 13-01-00589 and 13-01-97028-povolzhye, the Federal Target Program “Personnel” №14.B37.21.0361, and by the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Contract №14.B37.21.0863).
Citation:
Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov, “Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone”, Regul. Chaotic Dyn., 18:5 (2013), 521–538
\Bibitem{GonGonKaz13}
\by Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov
\paper Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 5
\pages 521--538
\mathnet{http://mi.mathnet.ru/rcd137}
\crossref{https://doi.org/10.1134/S1560354713050055}
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Linking options:
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