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.