2026/03/23 by Bernd von Mallinckrodt · 1 voice
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Complex Systems and Dynamics #Complex Systems and Time Series Analysis #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19183480
openalex publication_date 2026/03/23 · openalex created_date 2026/03/24 · openalex updated_date 2026/07/01
This preprint examines the mechanism-dependent behavior of structural and amplitude-based indicators in multivariate stochastic systems. Classical early warning signals (EWS), such as variance and lag-1 autocorrelation (AR(1)), are often treated as universal indicators of approaching critical transitions. However, their performance depends on the underlying dynamical mechanism. Using a controlled simulation of k=5 coupled stochastic variables over n=500 timesteps, we compare two noise regimes: (1) independent noise (control) and (2) partially shared (common-mode) noise, which induces structural compression. The system includes a gradually increasing coupling parameter, but no explicit bifurcation in the compression condition. Results show that variance and AR(1) exhibit no systematic differences between the two regimes. In contrast, the effective rank of the covariance matrix — used as a proxy for structural dimensionality — is consistently lower under shared-noise conditions, indicating a reduction in effective degrees of freedom. No monotonic pre-transition signal is observed in either case. These findings demonstrate that structural metrics can distinguish between qualitatively different system organizations even when amplitude-based indicators fail to do so. Effective rank therefore functions as a mechanism-sensitive structural diagnostic rather than a universal early warning signal. The study highlights the importance of aligning diagnostic metrics with the underlying mechanism of system change and positions structural indicators as a complementary tool alongside classical EWS in complex system analysis. early warning signals effective rank structural compression critical transitions multivariate stochastic systems mechanism-dependent diagnostics covariance structure complex systems