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In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often…

Fluid Dynamics · Physics 2026-03-26 Rohit Radhakrishnan , Prasana Kumar , Induja Pavithran , R. I. Sujith

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…

The progression of complex human diseases is associated with critical transitions across dynamical regimes. These transitions often spawn early-warning signals and provide insights into the underlying disease-driving mechanisms. In this…

Quantitative Methods · Quantitative Biology 2019-10-24 Pejman F. Ghalati , Satya S. Samal , Jayesh S. Bhat , Robert Deisz , Gernot Marx , Andreas Schuppert

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

Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by…

Dynamical Systems · Mathematics 2025-10-03 Paul A. Sanders , Robbin Bastiaansen

Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this…

Methodology · Statistics 2024-03-11 Giona Casiraghi , Georges Andres

Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding…

Machine Learning · Statistics 2025-09-30 Ioanna-Yvonni Tsaknaki , Fabrizio Lillo , Piero Mazzarisi

Epilepsy is a common neurological disorder characterized by abrupt seizures. Although seizures may appear random, they are often preceded by early warning signs in neural signals, notably, critical slowing down, a phenomenon in which the…

Systems and Control · Electrical Eng. & Systems 2024-11-12 Yuzhen Qin , Marcel van Gerven

Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…

Data Analysis, Statistics and Probability · Physics 2022-05-18 Sayantan Nag Chowdhury , Arnob Ray , Syamal K. Dana , Dibakar Ghosh

Early-warning signals of delicate design are always used to predict critical transitions in complex systems, which makes it possible to render the systems far away from the catastrophic state by introducing timely interventions. Traditional…

Machine Learning · Computer Science 2024-12-25 Shirui Bian , Zezhou Wang , Siyang Leng , Wei Lin , Jifan Shi

Climate extremes present escalating risks to agriculture intensifying the need for reliable multi-hazard early warning systems (EWS). The situation is evolving due to climate change and hence such systems should have the intelligent to…

Machine Learning · Computer Science 2025-08-01 Boyuan Zheng , Victor W. Chu

Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…

Adaptation and Self-Organizing Systems · Physics 2019-07-05 Deniz Eroglu , Matteo Tanzi , Sebastian van Strien , Tiago Pereira

An important paradigm in smart health is developing diagnosis tools and monitoring a patient's heart activity through processing Electrocardiogram (ECG) signals is a key example, sue to high mortality rate of heart-related disease. However,…

Signal Processing · Electrical Eng. & Systems 2018-11-02 Jiaming Chen , Ali Valehi , Abolfazl Razi

Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining…

Statistical Mechanics · Physics 2016-07-15 Victor Rodriguez-Mendez , Victor M. Eguiluz , Emilio Hernandez-Garcia , Jose J. Ramasco

We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two…

Data Analysis, Statistics and Probability · Physics 2015-06-18 Davide Faranda , Flavio Maria Emanuele Pons , Bérengère Dubrulle

Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points.…

Methodology · Statistics 2026-02-11 Sigrunn H. Sørbye , Eirik Myrvoll-Nilsen , Håvard Rue

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

In this study, we investigate prediction methods for an early warning system for a large STEM undergraduate course. Recent studies have provided evidence in favour of adopting early warning systems as a means of identifying at-risk…

History and Overview · Mathematics 2025-01-15 Emma Howard , Maria Meehan , Andrew Parnell

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…

Chaotic Dynamics · Physics 2014-03-13 Jesse Berwald , Marian Gidea

Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate…

Quantitative Methods · Quantitative Biology 2026-02-03 Xiaoai Xu , Yixuan Zhou , Xiang Zhou , Jingqiao Duan , Ting Gao