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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 5, Pages 521–538
DOI: https://doi.org/10.1134/S1560354713050055 (Mi rcd137) 		 
This article is cited in 81 scientific papers (total in 82 papers)

Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone

Alexander S. Gonchenkoa, Sergey V. Gonchenkoa, Alexey O. Kazakovab

a Research Institute of Applied Mathematics and Cybernetics, Nizhny Novgorod State University, ul. Ul’yanova 10, Nizhny Novgorod, 603005 Russia
b Institute of Computer Science, ul. Universitetskaya 1, Izhevsk, 426034 Russia
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DOI: https://doi.org/10.1134/S1560354713050055
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.
Keywords: celtic stone, nonholonomic model, strange attractor, discrete Lorenz attractor, Shilnikov-like spiral attractor, mixed dynamics.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00001
13-01-00589
13-01-97028-povolzhye
Ministry of Education and Science of the Russian Federation 14.B37.21.0361
14.B37.21.0863
This work was supported by the RFBR grants ¹11-01-00001, 13-01-00589 and 13-01-97028-povolzhye, the Federal Target Program “Personnel” ¹14.B37.21.0361, and by the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Contract ¹14.B37.21.0863).
Received: 25.06.2013
Accepted: 12.09.2013
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37N15, 37G35
Language: English
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
Citation in format AMSBIB
\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}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3117260}
\zmath{https://zbmath.org/?q=an:06292757}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000325810200005}
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    • This publication is cited in the following 82 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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