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Bistable Systems with Stochastic Noise: Virtues and Limits of Effective One-dimensional Langevin Equations : Volume 19, Issue 1 (03/01/2012)

By Lucarini, V.

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Book Id: WPLBN0003978167
Format Type: PDF Article :
File Size: Pages 14
Reproduction Date: 2015

Title: Bistable Systems with Stochastic Noise: Virtues and Limits of Effective One-dimensional Langevin Equations : Volume 19, Issue 1 (03/01/2012)  
Author: Lucarini, V.
Volume: Vol. 19, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2012
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Lucarini, V., Faranda, D., & Willeit, M. (2012). Bistable Systems with Stochastic Noise: Virtues and Limits of Effective One-dimensional Langevin Equations : Volume 19, Issue 1 (03/01/2012). Retrieved from http://hawaiilibrary.net/


Description
Description: Klimacampus, Institute of Meteorology, Hamburg Universität, Hamburg, Germany. The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

Summary
Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

Excerpt
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