Critical slowing down indicators

Fahimeh Nazarimehr1, Sajad Jafari1,2 , Matjaˇz Perc3,4,5 and Julien C. Sprott6

1 Biomedical Engineering Department, Amirkabir University of Technology - Tehran, Iran
2 Health Technology Research Institute, Amirkabir University of Technology - Tehran, Iran
3 Faculty of Natural Sciences and Mathematics, University of Maribor - Koroˇska cesta 160, 2000 Maribor, Slovenia
4 Dept. of Medical Research, China Medical University Hospital, China Medical University - Taichung, Taiwan
5 Complexity Science Hub Vienna - Josefst¨adterstraße 39, 1080 Vienna, Austria
6 Department of Physics, University of Wisconsin-Madison - Madison, WI 53706, USA

received 1 October 2020; accepted in final form 23 October 2020
published online 18 December 2020
PACS 89.75.-k – Complex systems
PACS 05.45.-a – Nonlinear dynamics and chaos

Abstract – Critical slowing down is considered to be an important indicator for predicting critical transitions in dynamical systems. Researchers have used it prolifically in the fields of ecology, biology, sociology, and finance. When a system approaches a critical transition or a tipping point, it returns more slowly to its stable attractor under small perturbations. The return time to the stable state can thus be used as an index, which shows whether a critical change is near or not. Based on this phenomenon, many methods have been proposed to determine tipping points, especially in biological and social systems, for example, related to epidemic spreading, cardiac arrhythmias, or
even population collapse. In this perspective, we briefly review past research dedicated to critical slowing down indicators and associated tipping points, and we outline promising directions for future research.

Ref: F. Nazarimehr, S. Jafari, M. Perc, and J. C. Sprott, European Physics Letters 132, 18001--1-7 (2020).

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