Bifurcation theory for SPDEs: finite-time Lyapunov exponents and amplitude equations

We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability.

For finite-time Lyapunov exponents we characterize regions depending on the distance from bifurcation and the noise strength where finite-time Lyapunov exponents are positive and thus detect changes in stability. One technical tool is the reduction of the essential dynamics of the infinite dimensional stochastic system to a simple ordinary stochastic differential equation, which is valid close to the bifurcation. This talk is based on joint works with Alex Blumenthal, Maximilian Engel and Dirk Blömker.