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Variations in stability revealed by temporal asymmetries in contraction of phase space flow
Empirical diagnosis of stability has received considerable attention, often focused on variance metrics for early warning signals of abrupt system change or delicate techniques measuring Lyapunov spectra. The theoretical foundation for the popular early warning signal approach has been limited to re...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7970983/ https://www.ncbi.nlm.nih.gov/pubmed/33707456 http://dx.doi.org/10.1038/s41598-021-84865-8 |
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author | Williams, Zachary C McNamara, Dylan E |
author_facet | Williams, Zachary C McNamara, Dylan E |
author_sort | Williams, Zachary C |
collection | PubMed |
description | Empirical diagnosis of stability has received considerable attention, often focused on variance metrics for early warning signals of abrupt system change or delicate techniques measuring Lyapunov spectra. The theoretical foundation for the popular early warning signal approach has been limited to relatively simple system changes such as bifurcating fixed points where variability is extrinsic to the steady state. We offer a novel measurement of stability that applies in wide ranging systems that contain variability in both internal steady state dynamics and in response to external perturbations. Utilizing connections between stability, dissipation, and phase space flow, we show that stability correlates with temporal asymmetry in a measure of phase space flow contraction. Our method is general as it reveals stability variation independent of assumptions about the nature of system variability or attractor shape. After showing efficacy in a variety of model systems, we apply our technique for measuring stability to monthly returns of the S&P 500 index in the time periods surrounding the global stock market crash of October 1987. Market stability is shown to be higher in the several years preceding and subsequent to the 1987 market crash. We anticipate our technique will have wide applicability in climate, ecological, financial, and social systems where stability is a pressing concern. |
format | Online Article Text |
id | pubmed-7970983 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-79709832021-03-19 Variations in stability revealed by temporal asymmetries in contraction of phase space flow Williams, Zachary C McNamara, Dylan E Sci Rep Article Empirical diagnosis of stability has received considerable attention, often focused on variance metrics for early warning signals of abrupt system change or delicate techniques measuring Lyapunov spectra. The theoretical foundation for the popular early warning signal approach has been limited to relatively simple system changes such as bifurcating fixed points where variability is extrinsic to the steady state. We offer a novel measurement of stability that applies in wide ranging systems that contain variability in both internal steady state dynamics and in response to external perturbations. Utilizing connections between stability, dissipation, and phase space flow, we show that stability correlates with temporal asymmetry in a measure of phase space flow contraction. Our method is general as it reveals stability variation independent of assumptions about the nature of system variability or attractor shape. After showing efficacy in a variety of model systems, we apply our technique for measuring stability to monthly returns of the S&P 500 index in the time periods surrounding the global stock market crash of October 1987. Market stability is shown to be higher in the several years preceding and subsequent to the 1987 market crash. We anticipate our technique will have wide applicability in climate, ecological, financial, and social systems where stability is a pressing concern. Nature Publishing Group UK 2021-03-11 /pmc/articles/PMC7970983/ /pubmed/33707456 http://dx.doi.org/10.1038/s41598-021-84865-8 Text en © The Author(s) 2021 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Williams, Zachary C McNamara, Dylan E Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title | Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title_full | Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title_fullStr | Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title_full_unstemmed | Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title_short | Variations in stability revealed by temporal asymmetries in contraction of phase space flow |
title_sort | variations in stability revealed by temporal asymmetries in contraction of phase space flow |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7970983/ https://www.ncbi.nlm.nih.gov/pubmed/33707456 http://dx.doi.org/10.1038/s41598-021-84865-8 |
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