| _version_ | 1866901088035143680 |
|---|---|
| author | Morris, Jamie |
| author_facet | Morris, Jamie |
| contents | <p>This work introduces the Genesis Protocol, a minimal dynamical framework describing threshold-triggered regime switching in coherent systems. The model consists of two regimes: a rigid, internally stabilizing state and a high-gain tracking state that aligns with external input. A critical coupling parameter determines the transition between these regimes.</p> <p>Below the threshold, the system evolves autonomously toward a stable equilibrium and remains insensitive to external input. Above the threshold, the system rapidly synchronizes with the input through a linear tracking mechanism. The transition is governed by a switching operator, resulting in a discontinuous change in system dynamics at the critical threshold.</p> <p>The framework is formulated using linear dynamics in each regime and requires only a small number of parameters. Analytical properties of stability and tracking behaviour are described, and the discontinuous transition is demonstrated through numerical simulations.</p> <p>This minimal model provides a testable mechanism for abrupt changes in responsiveness and may be relevant to biological, neural, and engineered systems exhibiting threshold-dependent behaviour.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19233626 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Genesis Protocol: Threshold-Triggered Regime Switching in Coherent Systems Morris, Jamie <p>This work introduces the Genesis Protocol, a minimal dynamical framework describing threshold-triggered regime switching in coherent systems. The model consists of two regimes: a rigid, internally stabilizing state and a high-gain tracking state that aligns with external input. A critical coupling parameter determines the transition between these regimes.</p> <p>Below the threshold, the system evolves autonomously toward a stable equilibrium and remains insensitive to external input. Above the threshold, the system rapidly synchronizes with the input through a linear tracking mechanism. The transition is governed by a switching operator, resulting in a discontinuous change in system dynamics at the critical threshold.</p> <p>The framework is formulated using linear dynamics in each regime and requires only a small number of parameters. Analytical properties of stability and tracking behaviour are described, and the discontinuous transition is demonstrated through numerical simulations.</p> <p>This minimal model provides a testable mechanism for abrupt changes in responsiveness and may be relevant to biological, neural, and engineered systems exhibiting threshold-dependent behaviour.</p> |
| title | The Genesis Protocol: Threshold-Triggered Regime Switching in Coherent Systems |
| url | https://doi.org/10.5281/zenodo.19233626 |