  A nonlinear model representing the tribological problem of a thin solid
lubricant layer between two sliding periodic surfaces is used to analyze the
phenomenon of hysteresis at pinning/depinning around a moving state rather than
around a statically pinned state. The cycling of an external driving force
F_ext is used as a simple means to destroy and then to recover the dynamically
pinned state previously discovered for the lubricant center-of-mass velocity.
De-pinning to a quasi-freely sliding state occurs either directly, with a
single jump, or through a sequence of discontinuous transitions. The
intermediate sliding steps are reminiscent of phase-locked states and
stick-slip motion in static friction, and can be interpreted in terms of the
appearance of travelling density defects in an otherwise regular arrangement of
kinks. Re-pinning occurs more smoothly, through the successive disappearance of
different travelling defects. The resulting bistability and multistability
regions may also be explored by varying mechanical parameters other than F_ext,
e.g. the sliding velocity or the corrugation amplitude of the sliders.
