Transition to a convective roll pattern as obtained from the stochastic center-manifold theory

We prove that the transition to a convective pattern in a Rayleigh-Bénard cell with a step in the heat input can be obtained by restricting the system to the locally attractive and locally invariant center manifold in phase space. The problem of providing the adequate scaling factor for the random source in the order-parameter equation is solved and the theoretical findings reproduce satisfactorily the experimentally measured time dependence for the convective heat flow.