2026/03/25 by Bernd von Mallinckrodt · 1 voice
Environmental Science · Physics and Astronomy · #Chaos control and synchronization #Climate variability and models #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19219962
openalex publication_date 2026/03/25 · openalex created_date 2026/03/26 · openalex updated_date 2026/07/01
This work introduces the Compression–Response Transition Index (CRTI), a ratio-based framework for the analysis of regime shifts in multivariate dynamical systems. CRTI is defined as T(t) = R(t) / Φ(t), linking adaptive capacity R(t), operationalized via return rates or autocorrelation-based recovery measures, to structural compression Φ(t), quantified through covariance geometry using effective rank. The framework is formulated with explicit operational definitions, a minimal coupled dynamical system in (R, Φ), and a preregistered empirical test design. Synthetic validation on controlled systems with known bifurcation structure demonstrates that the ratio T(t) can provide a more consistent and earlier monotonic signal of approaching regime transitions than its individual components. The analysis is complemented by a formal falsification criterion and direct comparison to established early warning signals, including variance and lag-1 autocorrelation. An empirical validation pipeline is specified for the Peter Lake whole-ecosystem transition, including a no-transition reference system, rolling-window estimation, and block-bootstrap inference. The study explicitly addresses methodological challenges such as covariance estimation bias, ratio instability, and window sensitivity, and treats universality as an open empirical question. This record serves as the consolidated flagship paper of a broader Zenodo research portfolio. Earlier records are retained for transparency but are structured as follows: Core foundations (recommended reading):- Sign Non-Invariance in Composite Early Warning Signals (Zenodo DOI)- Variance vs. Covariance Geometry in Early Warning Signals (Zenodo DOI)- Effective Rank as a Structural Indicator in Complex Systems (Zenodo DOI) Supporting technical notes (optional):- CRTI empirical validation pipeline and synthetic experiments- Boundary conditions of ratio-based early warning indicators- Methodological explorations of covariance-based metrics Superseded or redundant records:Earlier exploratory versions and overlapping drafts are preserved for completeness but are superseded by the present consolidated formulation. Readers should cite this record as the primary reference. Earlier Zenodo records provide supporting material where explicitly referenced. CRTI is presented as a testable structural complement to existing early warning signal frameworks, not as a universal law. early warning signals, regime shifts, critical transitions, complex systems, multivariate analysis, covariance structure, effective rank, adaptive capacity, Ornstein-Uhlenbeck process, return rate, autocorrelation, spectral entropy, bifurcation, saddle-node, separatrix, dynamical systems, statistical physics, ecological systems, network dynamics, CRTI