Distinguishing extreme events from nominal chaos

When considering climate change, one might say that extreme events, such as storms and heat waves, are becoming more common and intense. However, this statement raises questions regarding the definition of extreme events. After all, if extreme events lose their rarity, it may be tempting for researchers to revise their benchmarks and introduce arbitrariness into their fields.

Letellier et al. addressed this lack of consensus on the definition of extreme events, pointing out how statistical thresholds often lack strong rationale. Instead, they propose combination of an amplitude threshold with a timescale threshold — that is, atypical dynamics within a limited timeframe — to distinguish extreme events from nominal chaos.

“In principle, science should avoid seeing extreme events as simple systems, and people should be more careful while speaking about extreme events,” said author Christophe Letellier. “Unfortunately, humans consider their lifetimes as a typical timescale for systems in nature; this does not always apply.”

The authors validated their definition of extreme events against two chaotic systems, a 3D jerk system and a 9D fluid convection model, by examining their amplitude oscillations and return maps. In doing so, they noted how extreme events can only be distinguished from nominal chaos through considering entire bifurcation diagrams.

“For speaking about extreme events, it is necessary to know quite well the nominal dynamics of the system,” said Letellier. “This is particularly challenging for systems in nature.”

In future works, the authors intend to explore the possibility of characterizing extreme events in climate patterns, cardiac variability, and mechanical ventilation dynamics based on limited datasets, which would shine light into the underlying dynamics of these fields.

Source: “To be an extreme event or not: That is the question,” by Christophe Letellier, Léandre Kamdjeu Kengne, Manyu Zhao, and Ludovico Minati, Chaos (2025). The article can be accessed at https://doi.org/10.1063/5.0273928 .