论文标题
使用时间1形式从观察到的轨迹估算阶段
Estimating Phase from Observed Trajectories Using the Temporal 1-Form
论文作者
论文摘要
振荡器本质上是普遍存在的，通常与控制振荡器长期动力学的渐近阶段的存在有关。 ％我们表明，可以使用精心选择的串联扩展来估算渐近阶段，该序列的扩展直接计算相响应曲线并提供算法来估计该系列的共效应。与所有先前可用的数据驱动相位估计方法不同，我们的算法可以：（i）使用比周期短得多的观察值； （ii）在可用的足够数据的任何正向不变区域内恢复阶段； （iii）恢复控制弱振荡器耦合的相响应曲线（PRC-S）； （iv）显示等质曲率，并恢复等位几何的非线性特征。我们的方法可能会在需要从测量或模拟的时间序列构建振荡器动力学模型的任何地方找到应用。
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series expansion which directly computes the phase response curve and provide an algorithm for estimating the co-efficients of this series. Unlike all previously available data driven phase estimation methods, our algorithm can: (i) use observations that are much shorter than a cycle; (ii) recover phase within any forward invariant region for which sufficient data are available; (iii) recover the phase response curves (PRC-s) that govern weak oscillator coupling; (iv) show isochron curvature, and recover nonlinear features of isochron geometry. Our method may find application wherever models of oscillator dynamics need to be constructed from measured or simulated time-series.
