Fast chaos versus white noise: Entropy analysis and a Fokker-Planck model for the slow dynamics
type: Item
instance of: scholarly article
title: Fast chaos versus white noise: Entropy analysis and a Fokker-Planck model for the slow dynamics
zbMATH Open document ID: 1050.60092
author: Holger Kantz
author: Wolfram Just
author: Nilüfer Baba
author: Katrin Gelfert
author: Anja Riegert
published in: Physica D
publication date: 2004-08-10T00:00:00Z
review text: The authors are interested in the distinction between deterministic chaos and noise, which is not easy at the level of observation. With this in mind, they consider two different settings. In the first one they study scale dependent dynamical entropies, and conclude that the chaotic entropy may appear as bounded or not (and then noisy), depending on which order two limits are taken. The second setting is a simple example of dynamical system, given by equations of type \[ {dx\over dt}= f(x,y),\quad \varepsilon{dy\over dt}= g(x,y), \] where the small parameter \(\varepsilon\) allows to distinguish between the slow variable \(x\) and the fast variable \(y\). They conclude (as is well known for a long time by mathematicians) that (under unformulated ergodic assumptions) the slow behavior is approximately diffusive. The whole paper is written in an informative, physician style.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 37M10
zbMATH DE Number: 2085458
zbMATH Keywords: deterministic chaos
zbMATH Keywords: time series
zbMATH Keywords: entropy
zbMATH Keywords: noise
zbMATH Keywords: real diffusion
MaRDI profile type: Publication
full work available at URL: j.physd.2003.09.006
OpenAlex ID: W2019757014
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DOI: 10.1016/J.PHYSD.2003.09.006
description: scientific article; zbMATH DE number 2085458