Geometric early warning indicator from stochastic separatrix structure in a random two-state ecosystem model
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917383507017728 |
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| author | Shi, Yuzhu Serdukova, Larissa Zheng, Yayun Petrovskii, Sergei Lucarini, Valerio |
| author_facet | Shi, Yuzhu Serdukova, Larissa Zheng, Yayun Petrovskii, Sergei Lucarini, Valerio |
| contents | Under-ice blooms in the Arctic can develop rapidly under conditions where conventional early warning signals based on critical slowing down fail due to strong noise or limited observational records. We analyze noise-induced transitions in a temperature phytoplankton stochastic differential equation model exhibiting bistability between background and bloom states. The committor function defines a stochastic separatrix as its 1/2-isocommittor, and the normal width of the associated transition layer yields a geometric indicator via arc-length averaging. Under systematic variation of noise intensity, this indicator scales linearly with noise strength, while the logarithm of the mean first passage time follows the Freidlin-Wentzell asymptotic law. Eliminating the noise parameter produces an affine scaling between the logarithmic transition time and the inverse square of the geometric indicator. The relation is robust under variations in discretization, neighborhood definition, and diffusion structure, and holds in the weak noise regime where the transition-layer width scales linearly with noise strength. Unlike variance or lag-one autocorrelation, the geometric indicator remains well defined when rapid transitions preclude reliable time-series estimation. These results provide a geometrically interpretable precursor of bloom onset that may support model-based ecological monitoring in high-variability Arctic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08861 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric early warning indicator from stochastic separatrix structure in a random two-state ecosystem model Shi, Yuzhu Serdukova, Larissa Zheng, Yayun Petrovskii, Sergei Lucarini, Valerio Dynamical Systems Probability Chaotic Dynamics Populations and Evolution 37H20, 37N25, 60H10 Under-ice blooms in the Arctic can develop rapidly under conditions where conventional early warning signals based on critical slowing down fail due to strong noise or limited observational records. We analyze noise-induced transitions in a temperature phytoplankton stochastic differential equation model exhibiting bistability between background and bloom states. The committor function defines a stochastic separatrix as its 1/2-isocommittor, and the normal width of the associated transition layer yields a geometric indicator via arc-length averaging. Under systematic variation of noise intensity, this indicator scales linearly with noise strength, while the logarithm of the mean first passage time follows the Freidlin-Wentzell asymptotic law. Eliminating the noise parameter produces an affine scaling between the logarithmic transition time and the inverse square of the geometric indicator. The relation is robust under variations in discretization, neighborhood definition, and diffusion structure, and holds in the weak noise regime where the transition-layer width scales linearly with noise strength. Unlike variance or lag-one autocorrelation, the geometric indicator remains well defined when rapid transitions preclude reliable time-series estimation. These results provide a geometrically interpretable precursor of bloom onset that may support model-based ecological monitoring in high-variability Arctic systems. |
| title | Geometric early warning indicator from stochastic separatrix structure in a random two-state ecosystem model |
| topic | Dynamical Systems Probability Chaotic Dynamics Populations and Evolution 37H20, 37N25, 60H10 |
| url | https://arxiv.org/abs/2603.08861 |