- 01-290 Nils Berglund and Barbara Gentz
- The effect of additive noise on dynamical hysteresis
Jul 27, 01
(auto. generated ps),
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Abstract. We investigate the properties of hysteresis cycles produced by a
one-dimensional, periodically forced Langevin equation. We show that
depending on amplitude and frequency of the forcing and on noise intensity,
there are three qualitatively different types of hysteresis cycles. Below a
critical noise intensity, the random area enclosed by hysteresis cycles is
concentrated near the deterministic area, which is different for small and
large driving amplitude. Above this threshold, the area of typical
hysteresis cycles depends, to leading order, only on the noise intensity.
In all three regimes, we derive mathematically rigorous estimates for
expectation, variance, and the probability of deviations of the
hysteresis area from its typical value.