Variations in stability revealed by temporal asymmetries in contraction of phase space flow

Abstract 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 limi...

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Autores principales:	Zachary C Williams, Dylan E McNamara
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/48c6f836f15d422693aec9e89f8d16fa
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spelling	oai:doaj.org-article:48c6f836f15d422693aec9e89f8d16fa2021-12-02T13:30:11ZVariations in stability revealed by temporal asymmetries in contraction of phase space flow10.1038/s41598-021-84865-82045-2322https://doaj.org/article/48c6f836f15d422693aec9e89f8d16fa2021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-84865-8https://doaj.org/toc/2045-2322Abstract 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.Zachary C WilliamsDylan E McNamaraNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Zachary C Williams Dylan E McNamara Variations in stability revealed by temporal asymmetries in contraction of phase space flow
description	Abstract 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	article
author	Zachary C Williams Dylan E McNamara
author_facet	Zachary C Williams Dylan E McNamara
author_sort	Zachary C Williams
title	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_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_sort	variations in stability revealed by temporal asymmetries in contraction of phase space flow
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/48c6f836f15d422693aec9e89f8d16fa
work_keys_str_mv	AT zacharycwilliams variationsinstabilityrevealedbytemporalasymmetriesincontractionofphasespaceflow AT dylanemcnamara variationsinstabilityrevealedbytemporalasymmetriesincontractionofphasespaceflow
_version_	1718392972240748544

Variations in stability revealed by temporal asymmetries in contraction of phase space flow

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