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Nelin. Dinam., 2013, Volume 9, Number 1, Pages 77–89 (Mi nd371)  

This article is cited in 3 scientific papers (total in 3 papers)

On existence of Lorenz-like attractors in a nonholonomic model of Celtic stones

Alexander S. Gonchenko, Sergey V. Gonchenko

Research Institute for Applied Mathematics and Cybernetics, Nizhnii Novgorod, Russia

Abstract: We consider a nonholonomic model of movement of celtic stone on the plane. We show that, for certain values of parameters characterizing geometrical and physical properties of the stone, a strange Lorenz-like attractor is observed in the model. We have traced both scenarios of appearance and break-down of this attractor.

Keywords: Celtic stone, nonholonomic model, the Lorenz attractor, Lorenz-like attractor for diffeomorphisms, chaotic dynamics.

Full text: PDF file (768 kB)
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Document Type: Article
UDC: 517.925 + 517.3
MSC: 37J60, 37N15, 37G35
Received: 07.02.2013
Revised: 22.03.2013

Citation: Alexander S. Gonchenko, Sergey V. Gonchenko, “On existence of Lorenz-like attractors in a nonholonomic model of Celtic stones”, Nelin. Dinam., 9:1 (2013), 77–89

Citation in format AMSBIB
\Bibitem{GonGon13}
\by Alexander~S.~Gonchenko, Sergey~V.~Gonchenko
\paper On existence of Lorenz-like attractors in a nonholonomic model of Celtic stones
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 1
\pages 77--89
\mathnet{http://mi.mathnet.ru/nd371}


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    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    2. A. V. Borisov, A. O. Kazakov, S. P. Kuznetsov, “Nonlinear dynamics of the rattleback: a nonholonomic model”, Phys. Usp., 57:5 (2014), 453–460  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    3. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
  • Нелинейная динамика
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