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We use direct statistical simulation (DSS) to find the low-order statisticsof the well-known dynamical system, the Lorenz63 model. Instead of accumulatingstatistics from numerical simulation of the dynamical systems, we solve theequations of motion for the statistics themselves after closing them by makingseveral different choices for the truncation. Fixed points of the statisticsare obtained either by time evolving, or by iterative methods. Statistics soobtained are compared to those found by the traditional approach.

Direct statistical simulation of the Lorenz63 system