Stochastic attractor bifurcation for the two‐dimensional Swift‐Hohenberg equation

The main objectives of this article are to introduce stochastic parameterizing manifolds and to study the dynamical transitions of the two‐dimensional stochastic Swift‐Hohenberg equation. The study is based on the general framework developed by Chekroun, Liu and Wang. The detailed effect of the noise on the transition and on the stochastic low‐dimensional parameterization of the system is obtained.