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.
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