加性噪声对动态迟滞的影响
The effect of additive noise on dynamical hysteresis
摘要：
研究了一维周期性受迫朗之万方程产生的磁滞回线的性质。我们发现，根据振幅和频率的强迫和噪声强度，有三种不同类型的滞后循环。在临界噪声强度以下，由磁滞回线包围的随机区域集中在确定性区域附近，这对于小的和大的驱动幅度是不同的。在此阈值以上，典型的滞后循环的面积取决于，以领先的顺序，仅在噪声强度。在所有这三个制度，我们从数学上严格的估计，期望，方差，和滞后区的偏差从其典型值的概率。
英文摘要：
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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