Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis

TL;DR

This paper explores how non-Gaussian, heavy-tailed Le9vy stable noise influences stochastic dynamics, revealing that noise-induced phenomena like resonance and hysteresis persist even with infinite variance fluctuations.

Contribution

It provides a comprehensive overview of recent research on the effects of Le9vy stable noise on stochastic systems, highlighting the robustness of noise-induced phenomena under non-Gaussian conditions.

Findings

Noise-induced ordering persists with Le9vy noise

Phenomena like stochastic resonance are robust under heavy-tailed fluctuations

Le9vy noise can induce superdiffusive behavior in systems

Abstract

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 L\'evy walks, so called L\'evy 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. L\'evy 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 L\'evy 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.