| _version_ | 1866901110022733824 |
|---|---|
| author | von Mallinckrodt, Bernd |
| author_facet | von Mallinckrodt, Bernd |
| contents | <p>This paper introduces a formal framework for analyzing collapse in complex adaptive systems under a mechanism-dependent perspective. Classical early warning signals (EWS), such as critical slowing down (CSD), are widely used to anticipate critical transitions, but their validity relies on specific dynamical assumptions that are not universally satisfied.</p> <p> </p> <p>The proposed Constraint-Response Transition Index (CRTI) framework distinguishes between multiple collapse mechanisms, including bifurcation-driven dynamics and structural compression. Structural compression is defined as the progressive reduction of accessible system configurations due to accumulating constraints, leading to a loss of adaptive capacity without necessarily producing classical CSD signatures.</p> <p> </p> <p>The framework formalizes adaptive capacity (R) and structural compression (Φ) as theoretical constructs, operationalized through empirically computable proxies, and introduces the viability ratio T = R / Φ as a continuous diagnostic index. A minimal dynamical system (coupled ODEs) is used to illustrate how different collapse mechanisms generate distinct trajectories and early warning signal patterns.</p> <p> </p> <p>A key implication is that early warning signals are not universal indicators of collapse, but mechanism-conditional diagnostics. Synthetic numerical examples illustrate that CSD-based indicators may provide reliable signals in bifurcation-driven systems while remaining uninformative in structurally compressed regimes, where alternative metrics (e.g., effective rank reduction, spectral entropy, and T trajectories) provide earlier diagnostic information.</p> <p> </p> <p>The framework is positioned in relation to prior work in cybernetics (requisite variety), resilience theory (rigidity traps), and critical transitions research. A preregistered falsification protocol is provided to enable empirical testing of the framework using ecological time-series data.</p> <p> </p> <p>This version (v3.0) includes reviewer-level corrections, clarified proxy definitions, an explicit mechanism classification protocol, and illustrative numerical examples.</p> <p> </p> <p>Primary keywords:</p> <p> </p> <ul> <li>critical transitions</li> <li>early warning signals</li> <li>structural compression</li> <li>adaptive capacity</li> <li>mechanism-dependent collapse</li> </ul> <p> </p> <p> </p> <p>Method / theory keywords:</p> <p> </p> <ul> <li>dynamical systems</li> <li>bifurcation theory</li> <li>information theory</li> <li>entropy</li> <li>mutual information</li> </ul> <p> </p> <p> </p> <p>Application / bridge keywords:</p> <p> </p> <ul> <li>complex systems</li> <li>ecological systems</li> <li>resilience</li> <li>system collapse</li> <li>regime shifts</li> </ul> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19160681 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Mechanism-Dependent Collapse in Complex Systems: Structural Compression and the Limits of Early Warning Signals von Mallinckrodt, Bernd <p>This paper introduces a formal framework for analyzing collapse in complex adaptive systems under a mechanism-dependent perspective. Classical early warning signals (EWS), such as critical slowing down (CSD), are widely used to anticipate critical transitions, but their validity relies on specific dynamical assumptions that are not universally satisfied.</p> <p> </p> <p>The proposed Constraint-Response Transition Index (CRTI) framework distinguishes between multiple collapse mechanisms, including bifurcation-driven dynamics and structural compression. Structural compression is defined as the progressive reduction of accessible system configurations due to accumulating constraints, leading to a loss of adaptive capacity without necessarily producing classical CSD signatures.</p> <p> </p> <p>The framework formalizes adaptive capacity (R) and structural compression (Φ) as theoretical constructs, operationalized through empirically computable proxies, and introduces the viability ratio T = R / Φ as a continuous diagnostic index. A minimal dynamical system (coupled ODEs) is used to illustrate how different collapse mechanisms generate distinct trajectories and early warning signal patterns.</p> <p> </p> <p>A key implication is that early warning signals are not universal indicators of collapse, but mechanism-conditional diagnostics. Synthetic numerical examples illustrate that CSD-based indicators may provide reliable signals in bifurcation-driven systems while remaining uninformative in structurally compressed regimes, where alternative metrics (e.g., effective rank reduction, spectral entropy, and T trajectories) provide earlier diagnostic information.</p> <p> </p> <p>The framework is positioned in relation to prior work in cybernetics (requisite variety), resilience theory (rigidity traps), and critical transitions research. A preregistered falsification protocol is provided to enable empirical testing of the framework using ecological time-series data.</p> <p> </p> <p>This version (v3.0) includes reviewer-level corrections, clarified proxy definitions, an explicit mechanism classification protocol, and illustrative numerical examples.</p> <p> </p> <p>Primary keywords:</p> <p> </p> <ul> <li>critical transitions</li> <li>early warning signals</li> <li>structural compression</li> <li>adaptive capacity</li> <li>mechanism-dependent collapse</li> </ul> <p> </p> <p> </p> <p>Method / theory keywords:</p> <p> </p> <ul> <li>dynamical systems</li> <li>bifurcation theory</li> <li>information theory</li> <li>entropy</li> <li>mutual information</li> </ul> <p> </p> <p> </p> <p>Application / bridge keywords:</p> <p> </p> <ul> <li>complex systems</li> <li>ecological systems</li> <li>resilience</li> <li>system collapse</li> <li>regime shifts</li> </ul> <p> </p> |
| title | Mechanism-Dependent Collapse in Complex Systems: Structural Compression and the Limits of Early Warning Signals |
| url | https://doi.org/10.5281/zenodo.19160681 |