Approximation representation of parameterizing manifold and non-Markovian reduced systems for a stochastic Swift–Hohenberg equation

Abstract Approximation representation of parameterizing manifold and non-Markovian reduced systems for a stochastic Swift–Hohenberg equation with additive noise has been investigated. The corresponding backward–forward systems have been proposed, which can give such stochastic parameterizing manifold as pullback limits depending through the nonlinear terms on the time–history of the dynamics of the low modes when the latter is simply approximated by its stochastic linear component in a mean square sense. Then approximation representation of parameterizing manifold is given. Furthermore, according to it, the non-Markovian reduced systems can be derived to reach good modeling performances in practice.