THE ONSET OF CHAOS AND ROUTES TO CHAOS IN HIGH-DIMENSIONAL LORENZ SYSTEMS

摘要

The original 3D Lorenz model is one of the most celebrated nonlinear dynamical system. A number of attempts have been made to generalize this model to higher dimensions and investigate high-dimensional chaos. In this paper, the 3D Lorenz system is extended to higher dimensions by selecting higher-order horizontal and vertical modes in doubled Fourier expansions of a stream function and temperature variations. The selection of the modes is guided by the requirements that they must conserve energy in the dissipa-tionless limit and lead to systems that have only bounded solutions. The obtained results showed that the lowest-order Lorentz model that satisfies these criteria is a 8D system, and that the onset of chaos and routes to chaos in this high-dimensional system are different than that observed in the original Lorenz model. Physical explanation of these results is given.