标题： 从噪声同步振荡器中推断噪声强度和相位响应 显示英文标题

标题： Inference of noise intensity and phase response from noisy synchronous oscillators

摘要： 许多生物和微尺度系统在噪声环境中表现出同步性。 这种噪声振荡器及其同步性的理论已经得到发展并被实验验证，但推断噪声强度和相位响应并不总是直接的。 在本研究中，我们提出一个有用的公式，使我们能够推断与周期性外部激励同步的噪声振荡器的噪声强度和相位响应。 通过小噪声的渐近近似，我们表明噪声同步振荡器在噪声强度和可测量量之间满足一个简单的关系，即振荡相位的稳态分布和作为平均相位速度获得的稳态概率流，这通过系统的数值分析得到验证。 所提出的公式有助于在弱噪声环境中对同步振荡器进行统一的分析和设计。 显示英文摘要

摘要： Numerous biological and microscale systems exhibit synchronization in noisy environments. The theory of such noisy oscillators and their synchronization has been developed and experimentally demonstrated, but inferring the noise intensity and phase response is not always straightforward. In this study, we propose a useful formula that enables us to infer the noise intensity and phase response of a noisy oscillator synchronized with periodic external forcing. Through asymptotic approximations for small noise, we show that noisy synchronous oscillators satisfy a simple relationship among the noise intensity and measurable quantities, i.e., the stationary distribution of the oscillation phase and stationary probability current obtained as the average phase velocity, which is verified through systematic numerical analysis. The proposed formula facilitates a unified analysis and design of synchronous oscillators in weakly noisy environments.