ENSEMBLES OF THE LORENZ ATTRACTOR

The temporal evolution of small and large ensembles is examined for th e Lorenz equations. It is shown that a general closed system of ensemb le averaged equations can be developed for the Lorenz equations, indep endent of the size of the ensemble. The closure is based on the method of Rothmayer & Black (1993). The present formulation gives a determin istic set of equations for the description of ensembles of the Lorenz attractor. Large ensemble solutions of the strange attractor computed in this study are found to be regular, without the sensitive dependenc e on initial conditions which characterizes the individual chaotic mem bers of the ensemble.