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Regul. Chaotic Dyn., 2013, Volume 18, Issue 5, Pages 521–538 (Mi rcd137)  

This article is cited in 31 scientific papers (total in 32 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

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
Ministry of Education and Science of the Russian Federation 14.B37.21.0361
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).


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Document Type: Article
MSC: 37J60, 37N15, 37G35
Received: 25.06.2013
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
\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

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    13. A. S. Gonchenko, S. V. Gonchenko, “Retracted: Lorenz-like attractors in a nonholonomic model of a rattleback”, Nonlinearity, 28:9 (2015), 3403–3417  crossref  mathscinet  zmath  isi  scopus; retracted article see 30 (2017), c3
    14. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
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    18. A. S. Gonchenko, S. V. Gonchenko, “Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps”, Physica D, 337 (2016), 43–57  crossref  mathscinet  zmath  isi  scopus
    19. V. Kozlov, “The phenomenon of reversal in the Euler–Poincaré–Suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724  crossref  mathscinet  zmath  isi  scopus
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    21. S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Proc. Steklov Inst. Math., 297 (2017), 208–234  mathnet  crossref  crossref  mathscinet  isi  elib
    22. S. V. Gonchenko, D. V. Turaev, “On three types of dynamics and the notion of attractor”, Proc. Steklov Inst. Math., 297 (2017), 116–137  mathnet  crossref  crossref  mathscinet  isi  elib
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    28. S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007  crossref  mathscinet  isi  scopus
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    30. I. I. Ovsyannikov, V. D. Turaev, “Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model”, Nonlinearity, 30:1 (2017), 115–137  crossref  mathscinet  zmath  isi  scopus
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