The Onset of Chaos and Routes to Chaos in High-Dimensional Lorenz Systems

Z.E. Musielak and D. Roy (USA)

Keywords

Lorenz models, high-dimensional chaos, routes to chaos

Abstract

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 se lecting higher-order horizontal and vertical modes in dou bled Fourier expansions of a stream function and tempera ture 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 satisīŦes these criteria is a 8D sys tem, 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.

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