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arXiv · 2003.07174

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

Zachary C Williams·Dylan E McNamara
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Abstract

Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to relatively simple system changes such as bifurcating fixed points where variability is extrinsic to the steady state. There is currently no foundation and associated metric for empirically exploring stability 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.

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Zachary C Williams, Dylan E McNamara. 2020-02-28. Variations in stability revealed by temporal asymmetries in contraction of phase space flow. https://arxiv.org/abs/2003.07174

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