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Alexander Gonchenko

ul. Uljanova 10, Nizhny Novgorod 603005, Russia
Institute for Applied Mathematics and Cybernetics,


Gonchenko A. S., Gonchenko S. V., Kazakov A. O.
Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone
2013, vol. 18, no. 5, pp.  521-538
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
Citation: Gonchenko A. S., Gonchenko S. V., Kazakov A. O.,  Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone, Regular and Chaotic Dynamics, 2013, vol. 18, no. 5, pp. 521-538

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