2026/04/07 by Bernd von Mallinckrodt · 1 voice
Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Dynamics #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19452473
openalex publication_date 2026/04/07 · openalex created_date 2026/04/08 · openalex updated_date 2026/07/01
This preprint introduces the Compression–Response Transition Index (CRTI), a mechanism-specific framework for detecting structural precursors to critical transitions in complex systems. Classical early warning signals (EWS), such as rising variance and increasing autocorrelation, primarily capture amplitude-based changes associated with critical slowing down. CRTI complements these approaches by introducing a second diagnostic dimension: structural compression, defined as the progressive concentration of system dynamics into fewer effective modes. The framework combines a structural quantity Φ(t), derived from the spectral entropy (effective rank) of the covariance matrix, with a dynamic recovery proxy R(t), typically estimated via autoregressive modeling. The composite index T(t) = R(t) / Φ(t) is designed to detect regimes in which structural dimensionality decreases independently of amplitude fluctuations — a pattern not captured by conventional EWS metrics. Theoretical motivation is provided through the behavior of linearized systems near fold (saddle-node) bifurcations, where covariance structure becomes increasingly dominated by a single mode. A robustness discussion addresses finite-sample effects and introduces random matrix theory (Marchenko–Pastur distribution) as a baseline for distinguishing genuine structural compression from sampling artifacts. A conceptual illustration using a mechanical clock clarifies the interpretation of structural and dynamic constraints. CRTI is not proposed as a universal indicator. Its applicability is restricted to multivariate systems with sufficient data quality, where structural and dynamic signals are separable and fold-type bifurcation is a plausible transition mechanism. The framework is presented as a complement to established EWS methods and as a basis for future empirical validation. early warning signals, critical transitions, structural compression, effective rank, spectral entropy, covariance structure, fold bifurcation, complex systems, resilience, random matrix theory, Marchenko–Pastur, multivariate time series, dynamical systems, CRTI