  The long term aim is to use modern dynamical systems theory to derive
discretisations of noisy, dissipative partial differential equations. As a
first step we here consider a small domain and apply stochastic centre manifold
techniques to derive a model. The approach automatically parametrises subgrid
scale processes induced by spatially distributed stochastic noise. It is
important to discretise stochastic partial differential equations carefully, as
we do here, because of the sometimes subtle effects of noise processes. In
particular we see how stochastic resonance effectively extracts new noise
processes for the model which in this example helps stabilise the zero
solution.
