基于Koopman算子理论的随机振子渐近相位与振幅的定义及数据驱动重构
Definition and data-driven reconstruction of asymptotic phase and amplitudes of stochastic oscillators via Koopman operator theory
AI总结：
本文从Koopman算子理论视角推广随机振荡系统的渐近相位与振幅定义，提出基于时间序列数据的估计方法，验证了标准EDMD可重构含噪FitzHugh-Nagumo神经元模型的相位与振幅函数。
摘要：
渐近相位与振幅是极限环振子分析中的基础概念。本文简要回顾了这些量的定义，尤其是从Koopman算子理论视角对随机振荡系统的推广，并讨论了一种从随机振荡系统的时间序列数据估计渐近相位与振幅函数的数据驱动方法。我们证明，标准的扩展动态模态分解（Extended dynamic mode decomposition, EDMD）仅需时间序列数据，就能成功重构含噪声的FitzHugh-Nagumo神经元模型的相位与振幅函数。
英文摘要：
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.
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