Early warning of critical transitions: Distinguishing supercritical and subcritical bifurcations from noisy observations
Abstract
Early-warning methods can indicate that a system is approaching a loss of stability, but they do not usually reveal whether the approaching bifurcation is supercritical or subcritical. We investigate whether this distinction can be made from noisy pre-transition observations. For this investigation, we extend a regression-based stability method by including the leading cubic nonlinear term, whose sign is used to predict the bifurcation type. We test the method on a stochastic pitchfork model and a spatial stochastic Swift-Hohenberg equation. In both models, classification improves with longer observation horizons, closer proximity to the bifurcation, stronger noise, and larger nonlinear effects. However, these conditions are also linked to a higher risk of noise-induced tipping in the subcritical case. The useful early-warning window is therefore determined by a balance between obtaining enough information to identify the bifurcation type and doing so before noise-induced tipping becomes too likely. In spatially extended systems, we find that observing the full spatial field allows classification over shorter observation horizons, and performance improves when a broader range of spatial modes contributes to the observed dynamics. Altogether, we identify the conditions under which the method can reliably distinguish between supercritical and subcritical bifurcations.
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BibTeX
@misc{sanders2026early,
title = {{Early warning of critical transitions: Distinguishing supercritical and subcritical bifurcations from noisy observations}},
author = {Paul A. Sanders and Christian Kuehn and Bastian Hilder and Robbin Bastiaansen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38866},
eprint = {2610.38866},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38866},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Early warning of critical transitions: Distinguishing supercritical and subcritical bifurcations from noisy observations
AU - Paul A. Sanders
AU - Christian Kuehn
AU - Bastian Hilder
AU - Robbin Bastiaansen
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38866
UR - https://arxiv.org/abs/2610.38866
AB - Early-warning methods can indicate that a system is approaching a loss of stability, but they do not usually reveal whether the approaching bifurcation is supercritical or subcritical. We investigate whether this distinction can be made from noisy pre-transition observations. For this investigation, we extend a regression-based stability method by including the leading cubic nonlinear term, whose sign is used to predict the bifurcation type. We test the method on a stochastic pitchfork model and a spatial stochastic Swift-Hohenberg equation. In both models, classification improves with longer observation horizons, closer proximity to the bifurcation, stronger noise, and larger nonlinear effects. However, these conditions are also linked to a higher risk of noise-induced tipping in the subcritical case. The useful early-warning window is therefore determined by a balance between obtaining enough information to identify the bifurcation type and doing so before noise-induced tipping becomes too likely. In spatially extended systems, we find that observing the full spatial field allows classification over shorter observation horizons, and performance improves when a broader range of spatial modes contributes to the observed dynamics. Altogether, we identify the conditions under which the method can reliably distinguish between supercritical and subcritical bifurcations.
ER -