History-dependent phase slips and rectification of a few coupled oscillators system

History dependence of the phase slippage is investigated using coupled oscillator systems containing two and three degrees of freedom with repulsive interaction. In some situations, these systems possess two values of the minimal external force needed to realize phase slip, with that actually realized being determined by the direction of the slippage relative to the direction of the previous slippage. In particular, the minimal external force for the phase slip is smaller when the previous slippage was in the same direction than when it was in the opposite direction. Owing to this property, a particle can continue to move in a given direction even in the case that it is subject to an external force whose direction changes in time as in a ratchet system which is regarded as one of the simplest model of molecular motors. [Copyright &y& Elsevier]