In this work, the authors propose the Hilbert transform (HT)-based numerical method to analyse the time series of the circadian rhythms. They demonstrate the application of HT by taking both deterministic and stochastic time series that they get from the simulation of the fruit fly model Drosophila melanogaster and show how to extract the period, construct phase response curves, determine period sensitivity of the parameters to perturbations and build Arnold tongues to identify the regions of entrainment. They also derive a phase model that they numerically simulate to capture whether the circadian time series entrains to the forcing period completely (phase locking) or only partially (phase slips) or neither. They validate the phase model, and numerics with the experimental time series forced under different temperature cycles. Application of HT to the circadian time series appears to be a promising tool to extract the characteristic information about circadian rhythms.

中文翻译：

---

昼夜节律基因调控网络的基于希尔伯特变换的时间序列分析。

在这项工作中，作者提出了基于希尔伯特变换 (HT) 的数值方法来分析昼夜节律的时间序列。他们通过从果蝇模型 Drosophila melanogaster 的模拟中获得确定性和随机时间序列来演示 HT 的应用，并展示如何提取周期、构建相位响应曲线、确定参数对扰动的周期敏感性并构建Arnold 用舌头识别夹带区域。他们还推导出一个相位模型，通过数值模拟来捕捉昼夜节律时间序列是完全（相位锁定）还是部分（相位滑动）或两者都没有进入强迫周期。他们验证了相位模型，以及在不同温度循环下强制实验时间序列的数值。