  We investigate the stability of spatially uniform solutions for the
collisionless dynamics of a fermionic superfluid. We demonstrate that, if the
system size is larger than the superfluid coherence length, the solution
characterized by a periodic in time order parameter is unstable with respect to
spatial fluctuations. The instability is due to the parametric excitations of
pairing modes with opposite momenta. The growth of spatial modulations is
suppressed by nonlinear effects resulting in a state characterized by a random
superposition of wave packets of the superfluid order parameter. We suggest
that this state can be probed by spectroscopic noise measurements.
