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Current inversion in the Lévy ratchet.

We study the motion of an overdamped test particle in a static periodic potential lacking spatial symmetry under the influence of periodically modulated alpha -stable (Lévy) type noise. Due to the nonthermal character of the driving noise, the particle exhibits a motion with a preferred direction. The additional periodic modulation of the noise asymmetry changes the behavior of the static "Lévy ratchet." For the fast rate of the noise asymmetry modulation, the Lévy ratchet behaves like the one driven by the symmetric alpha -stable noise. When the modulation period is larger, the nontrivial effects of the noise asymmetry on the behavior of the Lévy ratchet are visible. In particular, the current inversion is observed in the system at hand. The properties of the Lévy ratchet are studied by use of the robust measures of directionality, which are defined regardless of the type of the stochastic driving.