Ap. Rothmayer et Dw. Black, ENSEMBLES OF THE LORENZ ATTRACTOR, Proceedings - Royal Society. Mathematical and physical sciences, 441(1912), 1993, pp. 291-312
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.