The effect of additive noise on dynamical hysteresis

Nils Berglund and Barbara Gentz
Nonlinearity 15:605-632 (2002)

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.

2000 Mathematics Subject Classification: 37H20 (primary), 60H10, 34C55, 34E15, 82C31 (secondary).

Keywords and phrases: Dynamical systems, singular perturbations, hysteresis cycles, scaling laws, non-autonomous stochastic differential equations, double-well potential, pathwise description, concentration of measure.

 

Journal Homepage Published article: 10.1088/0951-7715/15/3/305 MR1901095 Zbl1073.37061

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