2026/03/28 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.19282869
openalex publication_date 2026/03/28 · openalex created_date 2026/03/29 · openalex updated_date 2026/07/01
Description Early warning signals of collapse in complex systems are typically grounded in the theory of critical slowing down, where increasing variance and autocorrelation indicate an approaching bifurcation. These indicators implicitly assume that loss of stability or noise amplification are the primary mechanisms of system failure. This paper introduces a distinct mechanism: Structural Compression–Driven Collapse (M3). In this regime, systems remain locally stable and do not exhibit classical early warning signals, yet undergo functional failure due to a progressive reduction in accessible state space and a loss of independent response modes. We formalize this mechanism using two quantities: (1) structural compression Φ, defined via the effective rank of the empirical covariance matrix, and (2) adaptive capacity R, defined via the participation ratio of the singular value spectrum of the system’s Jacobian. We show that under specific conditions, Φ can increase and R can decrease monotonically while classical indicators such as variance and AR(1) remain uninformative. This defines a collapse pathway that is neither bifurcation-driven (M1) nor noise-amplified (M2), but structurally induced. The proposed Compression–Response Transition Index (CRTI), defined as T = R/Φ, is introduced as an interpretive diagnostic for this mechanism. Importantly, CRTI is not presented as a universal early warning indicator; its applicability is explicitly conditional on mechanism class, observational alignment, and functional specification. The framework provides:- a formal distinction between three collapse mechanisms (M1, M2, M3),- a covariance-geometric interpretation of structural fragility,- and a theoretical explanation for failure without classical early warning signals. Limitations are explicitly addressed, including dependence on observation window, projection bias, and the requirement of a system-specific functional definition of collapse. This work contributes a mechanism-level refinement of collapse theory in complex systems and establishes conditions under which structure, rather than instability, governs system failure. complex systems, collapse dynamics, early warning signals, critical slowing down, structural compression, covariance geometry, effective rank, adaptive capacity, dynamical systems, bifurcation theory, stochastic systems, resilience, system stability, projection effects, information theory