The effect of additive noise on dynamical hysteresis

Authors: Berglund N.1; Gentz B.2

Source: Nonlinearity, Volume 15, Number 3, 2002 , pp. 605-632(28)

Publisher: Institute of Physics Publishing

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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.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Department of Mathematics, ETH Z?rich, ETH Zentrum, 8092 Z?rich, Switzerland 2: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstra?e 39, 10117 Berlin, Germany

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