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Article

Об области существования дискретного аттрактора Лоренца в неголономной модели кельтского камня

Гонченко А. С., Самылина Е. А.

We consider the problem on the existence of discrete Lorenz attractors in a nonholonomic Celtic stone model. To this end, in two-parameter families of such models of certain types, the main local and global bifurcations  leading to both the appearance and destruction of the attractors are studied. In the plane of governing parameters (one of them is the angle of dynamical asymmetry of the stone, and the other is the total energy) , we construct the corresponding bifurcation diagram, where the region of existence of the discrete Lorenz attractor is shown and its boundaries are explained. We point out the similarities and differences in the scenarios of the emergence of the discrete Lorenz attractor in the nonholonomic model of Celtic stone and the attractor from the classical Lorenz model.