标题： 通过Koopman算子理论定义和数据驱动重构随机振荡器的渐近相位和幅值 显示英文标题

标题： Definition and data-driven reconstruction of asymptotic phase and amplitudes of stochastic oscillators via Koopman operator theory

摘要： 渐近相位和振幅是极限环振荡器分析中的基本概念。 在本文中，我们简要回顾这些量的定义，特别是从Koopman算子理论的角度对随机振荡系统的推广，并讨论一种数据驱动的方法，从随机振荡系统的时序数据中估计渐近相位和振幅函数。 我们证明，标准的扩展动态模态分解（EDMD）仅从噪声FitzHugh-Nagumo神经元模型的时序数据中就可以成功重建相位和振幅函数。 显示英文摘要

摘要： Asymptotic phase and amplitudes are fundamental concepts in the analysis of limit-cycle oscillators. In this paper, we briefly review the definition of these quantities, particularly a generalization to stochastic oscillatory systems from the viewpoint of Koopman operator theory, and discuss a data-driven approach to estimate the asymptotic phase and amplitude functions from time-series data of stochastic oscillatory systems. We demonstrate that the standard Extended dynamic mode decomposition (EDMD) can successfully reconstruct the phase and amplitude functions of the noisy FitzHugh-Nagumo neuron model only from the time-series data.