The effect of additive noise on dynamical hysteresis

Details The effect of additive noise on dynamical hysteresis The effect of additive noise on dynamical hysteresis

2001-07-27

arxiv.org/abs/math/0107199v1

Nonlinearity 15:605-632 (2002)

Mathematics

Dynamical Systems

30 pages, 5 figures

Scientific paper

10.1088/0951-7715/15/3/305

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.

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