Ratchet effect and the phenomenon of stochastic resonance (SR) are investigated numerically in different random systems. For a simple flashing ratchet model, it is shown that both the power spectrum amplitude and the mean mobility of the system vary nonmonotonically in similar manners with the increase of the noise intensity. And for a Brownian motor with stochastic state-jumping, fixing the noise level in an anisotropic potential and merely increasing the thermal fluctuation in a flat potential not only causes the increasing of the mean mobility to a saturated value, but also induce the spectrum-measured SR. However, increasing the noise intensities in two potentials simultaneously induces mobility-measured SR, but no spectrum-measured SR can be observed.
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