Regular and Chaotic Dynamics

, Volume 18, Issue 5, pp 521–538 | Cite as

Richness of chaotic dynamics in nonholonomic models of a celtic stone

  • Alexander S. Gonchenko
  • Sergey V. Gonchenko
  • Alexey O. Kazakov
Article

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 

MSC2010 numbers

37J60 37N15 37G35 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • Alexander S. Gonchenko
    • 1
  • Sergey V. Gonchenko
    • 1
  • Alexey O. Kazakov
    • 1
    • 2
  1. 1.Research Institute of Applied Mathematics and CyberneticsNizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Institute of Computer ScienceIzhevskRussia

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