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Article

Хаотическая динамика и мультистабильность в неголономной модели кельтского камня

Казаков А. О., Гонченко А. С., Гонченко С. В., Самылина Е. А.

We study dynamical properties of a Celtic stone moving along the plane. Both one- and two-parameter families of the corresponding nonholonomic models are considered, in which bifurcations are studied that lead to changing types of stable motions of the stone as well as to the onset of chaotic dynamics. It is shown that multistability phenomena are observed in such models when stable regimes of various types (regular and chaotic) can coexist in the phase space of the system. In the parameter space, the regions are constructed in which multistability is observed, and its types are described. We also show that chaotic dynamics of the nonholonomic model of Celtic stone can be very diverse. Here, in the corresponding parameter regions, there are observed both spiral strange attractors of various types, including the so-called discrete Shilnikov attractors, and mixed dynamics, when attractor and repeller intersect and almost coincide.