2026/04/11 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.19509849
openalex publication_date 2026/04/11 · openalex created_date 2026/04/12 · openalex updated_date 2026/07/01
This work introduces the Compression–Response Transition Index (CRTI), a composite early warning indicator for detecting critical transitions in complex systems. While classical early warning signals (EWS) are typically based on critical slowing down—manifested in rising variance and increasing autocorrelation—such univariate indicators may fail to capture structural changes in multivariate systems. CRTI combines two complementary components: (i) a structural measure Φ(t), defined as the exponential spectral entropy of a rolling covariance matrix and interpretable as a proxy for the effective dimensionality of the system, and (ii) a dynamical measure R(t), derived from autoregressive recovery rates and related to system responsiveness near equilibrium. The resulting composite index T(t) = R(t)/Φ(t) integrates covariance-based structural information with dynamical recovery behavior. The framework is designed for systems approaching fold (saddle-node) bifurcations under stochastic forcing. It is based on the hypothesis that covariance eigenvalues concentrate prior to observable dynamical instability, reflecting a reduction in effective dimensionality. Under these conditions, CRTI may provide early warning signals even when marginal variance and autocorrelation remain inconclusive. The approach is mechanism-specific and assumes multivariate observability, approximate local stationarity within rolling estimation windows, and well-behaved noise. CRTI is not intended as a universal early warning signal but as a structured, covariance-based complement to existing methods, particularly in high-dimensional systems where structural reorganization may precede detectable dynamical slowing down. early warning signals critical transitions complex systems critical slowing down multivariate time series covariance matrix spectral entropy effective dimensionality fold bifurcation saddle-node bifurcation nonlinear dynamics dynamical systems system stability tipping points structural indicators eigenvalues high-dimensional systems