Systematics of the Periodic Windows in the Lorenz Model and its Relation with the Antisymmetric Cubic Map^†

The Lorenz model and the antisymmetric cubic map enjoy the same discrete symmetry. A careful study of a one-dimensional bifurcation diagram obtained numerically from the Lorenz model reveals that the systematics of periodic windows is closely related to that of the cubic map. In addition, we determined the drift of the fundamental frequency and thus proposed a nomenclature for the periodic windows by associating an absolute period to each window, which in turn agrees with the corresponding word made of three letters for most of the observed periods.