2026/04/05 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.19426875
openalex publication_date 2026/04/05 · openalex created_date 2026/04/06 · openalex updated_date 2026/07/01
This paper introduces Structural Compression (Φ) as a geometrically grounded early warning signal for fold-type (saddle-node) critical transitions in complex dynamical systems. Classical early warning signals based on critical slowing down (CSD), such as rising variance and lag-1 autocorrelation, are widely used but remain mechanism-agnostic and primarily amplitude-based. They do not provide a structural account of how a system progressively loses resilience prior to a transition. To address this limitation, Structural Compression is defined as the normalized spectral entropy of a rolling covariance matrix, capturing the effective dimensionality of multivariate state-space dynamics. As a system approaches a fold bifurcation, variance concentrates along a critical mode, resulting in a measurable contraction of degrees of freedom reflected in decreasing Φ. The framework introduces the Compression–Response Transition Index (CRTI), defined as T = R̂ / Φ, where R̂ denotes adaptive response capacity derived from lag-1 autocorrelation of the leading principal component. A formal validity boundary is established via the Structural–Dynamic Separability (SDS) condition, requiring low correlation between Φ and R̂ for meaningful composite interpretation. Simulation results indicate that Φ declines and T rises consistently prior to fold-type bifurcations, while these patterns are not reproduced under Hopf bifurcation or noise-induced transition conditions. These findings support a mechanism-specific interpretation of early warning signals based on geometric structure rather than amplitude alone. This paper provides the primary theoretical formulation of the CRTI framework. All related extensions, methodological refinements, and domain applications build upon the definitions and boundary conditions established here. Limitations: The framework applies specifically to fold-type bifurcations and is not applicable to Hopf or noise-induced transitions. Results are based on simulation experiments and require empirical validation across independent datasets. No operational thresholds are defined. Preprint DOI: https://doi.org/10.5281/zenodo.19410081 early warning signals; structural compression; spectral entropy; critical transitions; CRTI; fold bifurcation; covariance dynamics; multivariate systems; resilience indicators; dynamical systems