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Regular version of the site

Article

Richness of Chaotic Dynamics in Nonholonomic Models of a Celtic Stone

Regular and Chaotic Dynamics. 2013. Vol. 18. No. 5. P. 521-538.
Гонченко А. С., Гонченко С. В., Kazakov A.

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.