2026/04/18 by Bernd von Mallinckrodt · 1 voice
Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Ecosystem dynamics and resilience #stochastic dynamics and bifurcation
paper · doi:10.5281/zenodo.19642418
openalex publication_date 2026/04/18 · openalex created_date 2026/04/19 · openalex updated_date 2026/07/01
This work presents a controlled benchmark for early-warning diagnostics in stochastic dynamical systems, focusing on the role of covariance structure under matched effective relaxation conditions. Two Ornstein–Uhlenbeck (OU) systems are compared: an isotropic system and an anisotropic system that differ only in covariance structure while sharing identical Wiener noise realizations and the same effective relaxation rate at every time. Within this setup, a standard scalar recovery metric (AR(1) on the leading principal component) is evaluated alongside a composite diagnostic combining autocorrelation with an effective-rank measure derived from spectral entropy. Across a parameter grid spanning anisotropy and rolling-window size, the scalar metric remains indistinguishable between systems, while the composite diagnostic exhibits systematic separation. The results demonstrate that covariance-structural differences can remain undetected by scalar recovery metrics under matched effective slowdown, but become observable when structural information is incorporated via effective rank. The construction is intentionally idealized to isolate this effect and does not claim generality beyond the studied regime. All simulations are fully reproducible. The repository includes the complete Python implementation, raw output data, and the figure used in the manuscript. early-warning signals, critical slowing down, Ornstein–Uhlenbeck process,covariance structure, effective rank, spectral entropy, AR(1),complex systems, stochastic dynamics, bifurcation indicators,multivariate time series, system stability, CRTI