  We estimate the finite-time Lyapunov exponents for a stochastic partial
differential equation driven by a fractional Brownian motion (fbm) with Hurst
index $H\in(0,1)$ close to a bifurcation of pitchfork type.
  We characterize regions depending on the distance from bifurcation, the Hurst
parameter of the fbm and the noise strength where finite-time Lyapunov
exponents are positive and thus indicate a change of stability. The results on
finite-time Lyapunov exponents are novel also for SDEs perturbed by fractional
noise.
