"Stochastic Dynamics near a Bifurcation - Amplitude Equations"

Dr. D. Blömker (RWTH Aachen)


Noise, for instance induced by thermal fluctuations, is natural in many physical models. Near a change of stability one can use the natural separation of time-scales for a multi-scale analysis, in order to derive amplitude equations, which are simpler equations describing the essential dynamics of the system. We discuss how noise enters these equations.
In this talk we consider as an example the stochastic Swift-Hohenberg equation, and give rigorous error estimates for the approximation via amplitude equations. This approximation extends to long time behaviour given by invariant measures, and allows for qualitative results on stochastic bifurcations. It also has applications in pattern formation below the threshold of instability.