Sigma-Lock and Twist Topology in Dynamical Systems: From Mandelbrot and Logistic to Lorenz, Gaia and Early-Warning
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2025
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| _version_ | 1866901343636029440 |
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| author | Ascher, Jörg |
| author_facet | Ascher, Jörg |
| contents | <p>This work introduces a twist-topological framework for early-warning signals in dynamical systems. We define <em>sigma-locks</em> as stable self-returning cycles and show how the corresponding sigma distances ($\delta$, $\delta_\sigma$) anticipate instability in logistic maps and the Lorenz flow before Lyapunov-based indicators. We extend the framework with triadic closure metrics to capture higher-order resilience. All methods are fully reproducible via the accompanying code and notebooks.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17882371 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Sigma-Lock and Twist Topology in Dynamical Systems: From Mandelbrot and Logistic to Lorenz, Gaia and Early-Warning Ascher, Jörg <p>This work introduces a twist-topological framework for early-warning signals in dynamical systems. We define <em>sigma-locks</em> as stable self-returning cycles and show how the corresponding sigma distances ($\delta$, $\delta_\sigma$) anticipate instability in logistic maps and the Lorenz flow before Lyapunov-based indicators. We extend the framework with triadic closure metrics to capture higher-order resilience. All methods are fully reproducible via the accompanying code and notebooks.</p> |
| title | Sigma-Lock and Twist Topology in Dynamical Systems: From Mandelbrot and Logistic to Lorenz, Gaia and Early-Warning |
| url | https://doi.org/10.5281/zenodo.17882371 |