期刊
REGULAR & CHAOTIC DYNAMICS
卷 18, 期 5, 页码 521-538出版社
PLEIADES PUBLISHING INC
DOI: 10.1134/S1560354713050055
关键词
celtic stone; nonholonomic model; strange attractor; discrete Lorenz attractor; Shilnikov-like spiral attractor; mixed dynamics
资金
- RFBR [11-01-00001, 13-01-00589, 13-01-97028-povolzhye]
- Federal Target Program Personnel [14.B37.21.0361]
- Federal Target Program Scientific and Scientific-Pedagogical Personnel of Innovative Russia [14.B37.21.0863]
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.
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