2026/03/07 by Bernd von Mallinckrodt · 1 voice
paper · doi:10.5281/zenodo.18899399
openalex publication_date 2026/03/07 · openalex created_date 2026/03/08 · openalex updated_date 2026/07/15
Description This preprint introduces the Compression–Resonance–Tension Index (CRTI), a minimal nonlinear dynamical framework for analyzing systemic collapse in complex adaptive systems. The work explores an alternative collapse mechanism that differs from the traditional disorder-driven paradigm frequently invoked in complexity science. In many real-world systems, collapse does not emerge primarily from increasing randomness or external shocks but from excessive structural optimization that progressively eliminates adaptive flexibility. The CRTI framework formalizes this phenomenon by modeling the interaction between two fundamental variables: structural compression (Φ) and adaptive reserve (Ω). Structural compression represents the degree of efficiency, rigidity, or constraint within a system. Adaptive reserve represents the available redundancy, diversity, or degrees of freedom that allow a system to respond to perturbations. The balance between these two quantities determines whether a system remains resilient or transitions toward collapse. The framework is implemented as a minimal nonlinear dynamical system defined by two coupled differential equations. Phase-space analysis reveals the existence of a stability corridor in which structure and reserve coexist in dynamic equilibrium. When structural compression increases beyond the regenerative capacity of the adaptive reserve, the system crosses a separatrix in phase space and enters a collapse trajectory characterized by the depletion of Ω. Within this framework, systemic collapse emerges as a process of reserve depletion under structural pressure, which we refer to as Singularization. In this state the system becomes highly efficient but loses the adaptive variance required for long-term stability. The model naturally reproduces several well-known early warning signals associated with critical transitions in complex systems, including: critical slowing down rising autocorrelation variance amplification monotonic increase of the collapse indicator χred = Φ / Ω These properties suggest that systemic fragility may often arise endogenously from internal optimization processes rather than from purely external disturbances. Although intentionally minimal, the CRTI framework provides a conceptual topology that may be applicable across a wide range of domains including: ecological systems experiencing biodiversity loss neural systems approaching pathological synchronization socio-economic systems characterized by hyper-optimized supply chains technological infrastructures with diminishing redundancy The present work focuses on establishing the mathematical structure of the model and its dynamical properties. Empirical calibration and domain-specific parameterization remain subjects for future research. The CRTI framework therefore offers a simplified theoretical tool for investigating the relationship between efficiency, resilience, and collapse in complex systems. Keywords (für Zenodo) Bitte genau diese Keywords eintragen: Complex Systems Nonlinear Dynamics Systemic Collapse Critical Transitions Early Warning Signals Adaptive Reserve Structural Compression System Stability Resilience Theory CRTI