Precursors of extreme events and critical transitions

TL;DR

This paper introduces a dynamical systems theory to predict extreme events and critical transitions by identifying a cascade of precursors in fast-slow nonlinear systems, validated through numerical tests.

Contribution

It presents a novel cascade-based framework for predicting extreme events and critical transitions with perfect accuracy, grounded in dynamical systems theory.

Findings

Precursors predict extreme events with 100% precision and recall.

A cascade of events precedes extreme events in fast-slow systems.

The theory is validated on low- and high-dimensional systems.

Abstract

We propose a theory based on dynamical systems to explain and predict the occurrence of extreme events, of which critical transitions form a subset. In fast-slow nonlinear systems, we identify a cascade of events preceding extreme events: (i) a slow regime, in which the fast covariant Lyapunov vectors (CLVs) are both tangent to the fast eigenvectors and remain transversal to the slow subspace; (ii) a transition regime, in which the fast eigenvalues become neutrally stable while the fast CLVs are no longer tangent to the fast eigenvectors; and (iii) a critical regime, in which a strong spectral gap in the eigenvalues causes both fast and slow CLVs to become tangent along the dominant fast direction, breaking the transversality between fast and slow subspaces. Building on this cascade, we propose two precursors to forewarn the occurrence of extreme events. We numerically test the theory and precursors on low- and higher-dimensional systems. The proposed precursors predict extreme events and critical transitions with 100% precision and recall. This work opens opportunities for time-forecasting extreme events using theoretically grounded precursors.