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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19233626 |
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Table of 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>