Decomposing Spectral and Phasic Differences in Nonlinear Features between Datasets,Physical Review Letters

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Decomposing Spectral and Phasic Differences in Nonlinear Features between Datasets
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-09-17 , DOI: 10.1103/physrevlett.127.124101
Pedro A M Mediano ₁ , Fernando E Rosas _{2,

3,

4} , Adam B Barrett ₅ , Daniel Bor ₁

Affiliation

When employing nonlinear methods to characterize complex systems, it is important to determine to what extent they are capturing genuine nonlinear phenomena that could not be assessed by simpler spectral methods. Specifically, we are concerned with the problem of quantifying spectral and phasic effects on an observed difference in a nonlinear feature between two systems (or two states of the same system). Here we derive, from a sequence of null models, a decomposition of the difference in an observable into spectral, phasic, and spectrum-phase interaction components. Our approach makes no assumptions about the structure of the data and adds nuance to a wide range of time series analyses.

中文翻译：

分解数据集之间非线性特征的频谱和相位差异

当使用非线性方法来表征复杂系统时，重要的是要确定它们在多大程度上捕获了无法通过更简单的光谱方法评估的真实非线性现象。具体来说，我们关注量化光谱和相位对两个系统（或同一系统的两个状态）之间观察到的非线性特征差异的影响的问题。在这里，我们从一系列空模型中推导出可观察到的差异分解为光谱、相位和光谱相位相互作用分量。我们的方法不对数据结构做出任何假设，并为广泛的时间序列分析增加了细微差别。

更新日期：2021-09-17

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