On the Region of Existence of a Discrete Lorenz Attractor in the Nonholonomic Model of a Celtic Stone

Abstract

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.