Direct statistical simulation of low-order dynamosystems

In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models dynamo action. The first model, which is a simple model solar and stellar action, third order has cubic nonlinearities while second only quadratic describes interaction convection an aperiodically reversing magnetic field. We show how DSS can be used to solve statistics these systems equations both in presence absence stochastic terms, by truncating cumulant hierarchy at either or order. compare different techniques solving statistics: timestepping, able locate stable solutions statistics, detection fixed points. develop complete methodology symbolic package Python deriving governing dynamic expansions. demonstrate that although points efficient accurate truncated order, addition higher terms leads inclusion many unstable may found point iterative methods. those cases, timestepping more robust protocol finding meaningful DSS.