Levy稳定噪声诱导跃迁：随机共振、共振激活和动态滞后
Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis
摘要：
随机动力学中噪声诱导效应分析的标准方法假设描述所分析系统与其复杂环境相互作用的噪声项具有高斯特性。关于所测量的可观测的动态和噪声的典型时间尺度之间存在时间尺度分离的附加假设允许外部波动被建模为时间上不相关的，因此是白色的。然而，在许多自然现象中，关于噪声的“高斯性”和“白度”的上述性质的假设可能被违反。在这种情况下，与表征一般形式的非马尔可夫或半马尔可夫Lévy游动的时空耦合相反，所谓的Lévy飞行对应于仍然可以被解释为白色的马尔可夫过程类，但是根据更一般的、无限可分的、稳定的和非高斯的定律分布。已知Lévy噪声驱动的非平衡系统表现出有趣的物理性质，并已在各种物理传输场景中表现出超扩散行为。在这里，我们提出了一个简短的概述，我们最近的调查，旨在了解Lévy白噪声扰动的影响下的随机动力学特性。我们发现，原型现象的噪声诱导的顺序是强大的，也可以检测到系统驱动的非高斯，重尾波动与无穷大的方差。
英文摘要：
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the abovementioned properties of "Gaussianity" and "whiteness" of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian Lévy walks, so called Lévy flights correspond to the class of Markov processes which still can be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. Lévy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed to understand features of stochastic dynamics under the influence of Lévy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by non-Gaussian, heavy-tailed fluctuations with infinite variance.
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