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A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical…

Physics and Society · Physics 2015-03-06 Christian Kuehn , Erik A. Martens , Daniel Romero

The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential…

Populations and Evolution · Quantitative Biology 2013-05-30 Carl Boettiger , Noam Ross , Alan Hastings

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…

Atmospheric and Oceanic Physics · Physics 2022-12-07 Daniel Dylewsky , Timothy M. Lenton , Marten Scheffer , Thomas M. Bury , Christopher G. Fletcher , Madhur Anand , Chris T. Bauch

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of…

Other Quantitative Biology · Quantitative Biology 2012-04-30 Carl Boettiger , Alan Hastings

Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…

Adaptation and Self-Organizing Systems · Physics 2017-02-28 Christian Kuehn , Gerd Zschaler , Thilo Gross

In this topical review, we present a brief overview of the different methods and measures to detect the occurrence of critical transitions in complex systems. We start by introducing the mechanisms that trigger critical transitions, and how…

Physics and Society · Physics 2023-07-05 Sandip V. George , Sneha Kachhara , G. Ambika

Financial markets of emerging economies are vulnerable to extreme and cascading information spillovers, surges, sudden stops and reversals. With this in mind, we develop a new online early warning system (EWS) to detect what is referred to…

Econometrics · Economics 2025-05-21 Artem Kraevskiy , Artem Prokhorov , Evgeniy Sokolovskiy

A broad range of natural and social systems from human microbiome to financial markets can go through critical transitions, where the system suddenly collapses to another stable configuration. Critical transitions can be unexpected, with…

Applications · Statistics 2022-05-17 Ville Laitinen , Leo Lahti

Lately, studying social dynamics in interacting agents has been boosted by the power of computer models, which bring the richness of qualitative work, while offering the precision, transparency, extensiveness, and replicability of…

Physics and Society · Physics 2022-06-17 Alyssa M Adams , Javier Fernandez , Olaf Witkowski

Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier…

Physics and Society · Physics 2023-06-27 Neil G. MacLaren , Prosenjit Kundu , Naoki Masuda

Complex systems can undergo critical transitions, where slowly changing environmental conditions trigger a sudden shift to a new, potentially catastrophic state. Early warning signals for these events are crucial for decision-making in…

Data Analysis, Statistics and Probability · Physics 2024-10-15 Zhiqin Ma , Chunhua Zeng , Yi-Cheng Zhang , Thomas M. Bury

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

Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions…

Machine Learning · Computer Science 2024-09-13 Yu Huang , Sebastian Bathiany , Peter Ashwin , Niklas Boers

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…

Machine Learning · Computer Science 2026-03-17 Xin Li , Qunxi Zhu , Chengli Zhao , Bolin Zhao , Xue Zhang , Xiaojun Duan , Wei Lin

Critical transitions - abrupt, often irreversible changes in system dynamics - arise across human and natural systems, often with catastrophic consequences. Real-world observations of such shifts remain scarce, preventing the development of…

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…

Chaotic Dynamics · Physics 2026-04-09 Smita Deb , Zheng-Meng Zhai , Mulugeta Haile , Ying-Cheng Lai

Key components of the Earth system can undergo abrupt and potentially irreversible transitions when the magnitude or rate of external forcing exceeds critical thresholds. In this study, we use the example of the Atlantic Meridional…

Computational Engineering, Finance, and Science · Computer Science 2025-09-09 Wenjie Zhang , Yu Huang , Sebastian Bathiany , Yechul Shin , Maya Ben-Yami , Suiping Zhou , Niklas Boers

Time perception research has advanced significantly over the years. However, some areas remain largely unexplored. This study addresses two such under-explored areas in timing research: (1) A quantitative analysis of time perception at an…

Human-Computer Interaction · Computer Science 2024-12-18 Amrapali Pednekar , Alvaro Garrido , Yara Khaluf , Pieter Simoens

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system…

Machine Learning · Computer Science 2020-12-04 Ling-Wei Kong , Hua-Wei Fan , Celso Grebogi , Ying-Cheng Lai

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
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