Generalized dynamical phase reduction for stochastic oscillators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916452901060608 |
|---|---|
| author | Houzelstein, Pierre Thomas, Peter J. Lindner, Benjamin Gutkin, Boris S. Pérez-Cervera, Alberto |
| author_facet | Houzelstein, Pierre Thomas, Peter J. Lindner, Benjamin Gutkin, Boris S. Pérez-Cervera, Alberto |
| contents | Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a self-contained stochastic phase equation of the form $\mathop{}\!\mathrm{d} ϕ= a(ϕ)\mathop{}\!\mathrm{d} t + \sqrt{2D(ϕ)}\,\mathop{}\!\mathrm{d} W(t)$ that is valid not only for noise-perturbed limit cycles, but also for noise-induced oscillations. We show that our reduction captures the asymptotic statistics of qualitatively different stochastic oscillators, and use it to infer their phase-response properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized dynamical phase reduction for stochastic oscillators Houzelstein, Pierre Thomas, Peter J. Lindner, Benjamin Gutkin, Boris S. Pérez-Cervera, Alberto Mathematical Physics Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a self-contained stochastic phase equation of the form $\mathop{}\!\mathrm{d} ϕ= a(ϕ)\mathop{}\!\mathrm{d} t + \sqrt{2D(ϕ)}\,\mathop{}\!\mathrm{d} W(t)$ that is valid not only for noise-perturbed limit cycles, but also for noise-induced oscillations. We show that our reduction captures the asymptotic statistics of qualitatively different stochastic oscillators, and use it to infer their phase-response properties. |
| title | Generalized dynamical phase reduction for stochastic oscillators |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2402.02856 |