Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals
- 1Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, China
- 2Business School, Southern University of Science and Technology, Shenzhen, China
Abstract
Early-warning indicators in ecosystems, neural activity, financial markets, and climate systems are often interpreted as evidence that a system is approaching a tipping point, typically understood as a bifurcation at which a previously stable state loses stability or disappears. Such indicators include increased variance, autocorrelation, and dimensional reduction. Here we identify a different mechanism that generates the same statistical signatures without any loss of stability. In stochastic non-normal dynamical systems, asymmetric interactions produce transient amplification that creates episodes of apparent instability despite the persistence of a stable attractor. We refer to these episodes as pseudo-bifurcations. Through analytical results, numerical simulations, and empirical evidence from brain dynamics during epileptic seizures, we show that pseudo-bifurcations reproduce the canonical early-warning signals commonly associated with bifurcation-induced tipping points. Crucially, these signatures arise while the underlying system remains dynamically stable and far from any bifurcation. These results demonstrate that widely used early-warning indicators are not uniquely diagnostic of tipping points. Instead, they may reflect the transient geometry of non-normal dynamics, which are ubiquitous in complex interacting systems. Early-warning indicators such as increased variance, autocorrelation, and dimensional reduction are often interpreted as signs that complex systems in ecology, neuroscience, finance, or climate are approaching a tipping point at which a stable state loses stability or disappears. Here, the authors demonstrate, using brain dynamics during epileptic seizures as an example case, that the same statistical signatures can arise from pseudo-bifurcations in stochastic non-normal systems, showing that these widely used indicators are not uniquely diagnostic of tipping points.
Related
- Early-warning signals of critical transitions in global ecoregions
- Projection, Memory, and the Validity of Scalar Early-Warning Signals: A Schur--Volterra Theory with an AMOC Application
- Review article: rainfall-induced landslide early warning systems through the lens of the early warnings for all framework – advances, gaps, and perspectives
- Prediction accuracy of available early warning systems for air pollution across WHO South-East Asia region: a systematic review
- A Prototype Probability Based Warning System for a Strong AMOC Decline
BibTeX
@article{troude2026pseudobifurcations,
title = {{Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals}},
author = {Virgile Troude and Sandro Claudio Lera and Ke Wu and Didier Sornette},
journal = {Communications Physics},
year = {2026},
month = jun,
doi = {10.1038/s42005-026-02703-7},
url = {https://doi.org/10.1038/s42005-026-02703-7},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Pseudo-bifurcations in stochastic non-normal systems and the limits of early-warning signals
AU - Virgile Troude
AU - Sandro Claudio Lera
AU - Ke Wu
AU - Didier Sornette
PY - 2026
DA - 2026/06/04
JO - Communications Physics
DO - 10.1038/s42005-026-02703-7
UR - https://doi.org/10.1038/s42005-026-02703-7
AB - Early-warning indicators in ecosystems, neural activity, financial markets, and climate systems are often interpreted as evidence that a system is approaching a tipping point, typically understood as a bifurcation at which a previously stable state loses stability or disappears. Such indicators include increased variance, autocorrelation, and dimensional reduction. Here we identify a different mechanism that generates the same statistical signatures without any loss of stability. In stochastic non-normal dynamical systems, asymmetric interactions produce transient amplification that creates episodes of apparent instability despite the persistence of a stable attractor. We refer to these episodes as pseudo-bifurcations. Through analytical results, numerical simulations, and empirical evidence from brain dynamics during epileptic seizures, we show that pseudo-bifurcations reproduce the canonical early-warning signals commonly associated with bifurcation-induced tipping points. Crucially, these signatures arise while the underlying system remains dynamically stable and far from any bifurcation. These results demonstrate that widely used early-warning indicators are not uniquely diagnostic of tipping points. Instead, they may reflect the transient geometry of non-normal dynamics, which are ubiquitous in complex interacting systems. Early-warning indicators such as increased variance, autocorrelation, and dimensional reduction are often interpreted as signs that complex systems in ecology, neuroscience, finance, or climate are approaching a tipping point at which a stable state loses stability or disappears. Here, the authors demonstrate, using brain dynamics during epileptic seizures as an example case, that the same statistical signatures can arise from pseudo-bifurcations in stochastic non-normal systems, showing that these widely used indicators are not uniquely diagnostic of tipping points.
SN - 2399-3650
ER -