Abstract
The temporal evolution of small and large ensembles is examined for the Lorenz equations. It is shown that a general closed system of ensemble averaged equations can be developed for the Lorenz equations, independent of the size of the ensemble. The closure is based on the method of Rothmayer & Black (1993). The present formulation gives a deterministic 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 dependence on initial conditions which characterizes the individual chaotic members of the ensemble.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
