In this work, we consider the problem of existence of discrete Lorenz attractors in the nonholonomic model of a Celtic stone. To this end, the main local and global bifurcations leading to the appearance and destruction of the attractors are studied in two-parameter families of such models of certain types. The corresponding bifurcation diagram, in which the region of existence of a discrete Lorenz attractor is shown and its boundaries are described, is obtained on the plane of the governing parameters (the angle of dynamic asymmetry of the stone–the total-energy value). The similarities and differences in the scenarios of the appearance of a discrete Lorenz attractor in the nonholonomic model of a Celtic stone and attractor in the classical Lorenz model are found.

中文翻译：

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凯尔特石非完整模型中离散洛伦兹吸引子的存在区域

在这项工作中，我们考虑了在凯尔特石头的非完整模型中存在离散洛伦兹吸引子的问题。为此，在某些类型的此类模型的双参数族中研究了导致吸引子出现和破坏的主要局部和全局分叉。相应的分岔图，其中显示了离散洛伦兹吸引子的存在区域并描述了其边界，是在控制参数（石头的动态不对称角度 - 总能量值）的平面上获得的。发现了凯尔特石头非完整模型中离散洛伦兹吸引子出现与经典洛伦兹模型中吸引子出现的场景的异同。