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Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on…

Populations and Evolution · Quantitative Biology 2012-10-04 Carl Boettiger , Alan Hastings

Early warning systems (EWSs) are critical for forecasting and preventing economic and financial crises. EWSs are designed to provide early warning signs of financial troubles, allowing policymakers and market participants to intervene…

General Finance · Quantitative Finance 2023-10-03 Ali Namaki , Reza Eyvazloo , Shahin Ramtinnia

There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…

Dynamical Systems · Mathematics 2026-03-30 Florian Suerhoff , Andreas Morr , Sebastian Bathiany , Niklas Boers , Christian Kuehn

Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…

Statistical Mechanics · Physics 2021-10-26 George I. Hagstrom , Simon A. Levin

Critical transitions are the abrupt shifts between qualitatively different states of a system, and they are crucial to understanding tipping points in complex dynamical systems across ecology, climate science, and biology. Detecting these…

Machine Learning · Computer Science 2026-03-06 Swadesh Pal , Roderick Melnik

Real-life systems often experience regime shifts. An early warning signal (EWS) is a quantity that attempts to anticipate such a regime shift. Because complex systems of practical interest showing regime shifts are often dynamics on…

Physics and Society · Physics 2025-05-23 Shilong Yu , Neil G. MacLaren , Naoki Masuda

The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…

Disordered Systems and Neural Networks · Physics 2026-02-11 A. V. Goltsev , S. N. Dorogovtsev

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…

Machine Learning · Statistics 2024-04-08 Lingyu Feng , Ting Gao , Wang Xiao , Jinqiao Duan

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…

Computational Physics · Physics 2024-08-08 Daniel Dylewsky , Madhur Anand , Chris T. Bauch

This study constructs an integrated early warning system (EWS) that identifies and predicts stock market turbulence. Based on switching ARCH (SWARCH) filtering probabilities of the high volatility regime, the proposed EWS first classifies…

Econometrics · Economics 2019-12-02 Peiwan Wang , Lu Zong , Ye Ma

In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modelling. Modelling efforts often focus on predicting whether diseases are likely to be eliminated or, instead,…

Populations and Evolution · Quantitative Biology 2026-01-22 Joshua Looker , Kat S. Rock , Louise Dyson

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very…

Data Analysis, Statistics and Probability · Physics 2024-07-12 Klaus Lehnertz

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

Data Analysis, Statistics and Probability · Physics 2023-06-28 Jacob D. Baxley , David R. Lambert , Mauro Bologna , Bruce J. West , Paolo Grigolini

Climate change and natural disasters are recognized as worldwide challenges requiring complex and efficient ecosystems to deal with social, economic, and environmental effects. This chapter advocates a holistic approach, distinguishing…

Computers and Society · Computer Science 2025-06-25 Fuzel Shaik , Getnet Demil , Mourad Oussalah

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…

Data Analysis, Statistics and Probability · Physics 2022-12-14 Martin Heßler , Oliver Kamps

Social ecological systems are often difficult to investigate and manage because of their inherent complexity1. Small variations in external drivers can lead to abrupt changes associated with instabilities and bifurcations in the underlying…

Populations and Evolution · Quantitative Biology 2017-02-08 Samir Suweis , Paolo D'Odorico

Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the…

Dynamical Systems · Mathematics 2025-11-25 Yuta Miyauchi , Masahiro Ikeda , Yoshinobu Kawahara

Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…

Pattern Formation and Solitons · Physics 2021-01-29 Induja Pavithran , R. I. Sujith

Stemming from physics and later applied to other fields such as ecology, the theory of critical transitions suggests that some regime shifts are preceded by statistical early warning signals. Reddit's r/place experiment, a large-scale…

Physics and Society · Physics 2026-03-23 Guillaume Falmagne , Anna B. Stephenson , Simon A. Levin

Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the…

Dynamical Systems · Mathematics 2016-09-26 Paul Ritchie , Jan Sieber