  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 bifurcations. 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.
