2026/04/03 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.19408113
openalex publication_date 2026/04/03 · openalex created_date 2026/04/04 · openalex updated_date 2026/07/01
This preprint introduces Structural Compression (Φ) as a mechanism-specific early warning signal for critical transitions in multivariate systems. Classical early warning signals (EWS), such as increasing variance and rising lag-1 autocorrelation, are grounded in the theory of critical slowing down and have been widely validated for systems approaching bifurcation-driven tipping points. However, these indicators may fail in scenarios where transitions are preceded by structural reorganisation rather than amplitude amplification. Structural Compression (Φ) is defined as the exponential of the spectral entropy of the rolling covariance matrix and can be interpreted as the effective dimensionality of a system’s covariance structure. The central hypothesis is that certain pre-transition regimes are characterised by a measurable loss of effective degrees of freedom, detectable through changes in the covariance spectrum. The approach is evaluated in controlled simulation experiments representing two mechanism classes: (M1) classical bifurcation scenarios, where variance-based indicators are informative, and (M2) structural compression regimes, where classical EWS remain uninformative. Results indicate that Φ provides an informative signal in M2 scenarios while remaining consistent with classical indicators in M1 settings. The contribution is explicitly limited in scope and positioned as a complement to existing early warning methodologies rather than a universal replacement. Limitations, including sensitivity to window length, high-dimensional estimation constraints, and projection effects, are discussed. early warning signals, critical transitions, structural compression, spectral entropy, covariance structure, effective dimensionality, multivariate systems, critical slowing down, tipping points, complex systems