随机振荡器的广义动力学相位约化
Generalized dynamical phase reduction for stochastic oscillators
AI总结：
针对随机振荡器的相位约化难题，本文提出可导出自洽随机相位方程的广义方法，统一刻画噪声扰动极限环与噪声诱导振荡，并据此推断相位响应特性。
摘要：
相位约化是研究耦合振荡器和受驱振荡器的重要工具。如何将相位约化推广到随机振荡器，仍是一个被积极讨论的问题。在本工作中，我们提出一种方法，用于推导形式为 $\mathop{}\\!\mathrm{d} ϕ= a(ϕ)\mathop{}\\!\mathrm{d} t + \sqrt{2D(ϕ)}\\,\mathop{}\\!\mathrm{d} W(t)$ 的自洽随机相位方程；该方程不仅适用于受噪声扰动的极限环，也适用于噪声诱导振荡。我们表明，我们的约化能够捕捉性质上不同的随机振荡器的渐近统计量，并利用它推断其相位响应特性。
英文摘要：
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.
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