2008/10/29 by Bartłomiej Dybiec, Bartlomiej Dybiec, Ewa Gudowska-Nowak · 1 citation
Environmental Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Ecosystem dynamics and resilience #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/2009/05/p05004
published as J. Stat. Mech. P05004 (2009) · 7 pages, 8 figures
arxiv created 2008/10/29 · openalex publication_date 2009/05/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 above mentioned 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 can still 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 at understanding 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 memoryless, non-Gaussian, heavy-tailed fluctuations with infinite variance.