2026/03/30 by Bernd von Mallinckrodt · 1 voice
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19329813
openalex publication_date 2026/03/30 · openalex created_date 2026/03/31 · openalex updated_date 2026/07/01
Early warning signals (EWS) of critical transitions—such as rising variance and autocorrelation—are widely used to anticipate abrupt changes in complex systems. However, their empirical performance is inconsistent, with frequent cases of signal suppression or even sign inversion prior to transition. This paper demonstrates that such failures can arise as a necessary consequence of observation geometry. Considering a high-dimensional dynamical system observed through a dimension-reducing mapping, we derive an explicit detectability bound linking the observability of EWS to the alignment between the system’s critical mode and the observation subspace. The central result expresses observable signal strength through a dimensionless ratio combining geometric alignment and dynamical growth rates, yielding a threshold condition under which early warning signals are attenuated, suppressed, or sign-inverted. The analysis shows that EWS failure is not primarily driven by noise, sampling limitations, or estimator choice, but by a structural mismatch between the evolving critical mode and the fixed observation mapping. In particular, sign inversion becomes more likely when the rate of geometric misalignment exceeds the rate of variance growth, a condition that can arise generically as systems approach critical transitions. This provides a unified geometric explanation for the mechanism-dependent reliability of early warning signals and establishes a quantitative framework for assessing their detectability under projection. The results are model-independent, analytically derived, and directly testable in both simulated and empirical systems. early warning signals, critical transitions, complex systems, dynamical systems, covariance structure, projection geometry, detectability bound, variance scaling, critical slowing down, observability, eigenvector alignment, dimensionality reduction, signal detection, bifurcation theory, nonlinear systems