  Spatially localized states play an important role in transition to turbulence
in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203
(2012)). Despite the fact that some of them are attractors on the separatrix
between laminar and turbulent flows, little is known of their dynamics. We
investigate here the temporal dynamics of such steady spatially localized
solutions in the context of plane Couette flow. These solutions exist on
oscillating branches in parameter space. We consider the saddle-nodes of these
branches as initial conditions of simulations run with offset Reynolds numbers.
We observe a relaminarization regime mostly characterized by deterministic
dynamics and identify within this regime the existence of parameter intervals
in which the results are stochastic and long-lived chaotic transients are
observed. These results are obtained below the threshold for transition, shed
light on the emergence of stochasticity in transitional plane Couette flow and
will likely inform a range of shear flow configurations.
