论文标题
振荡器同步中的Koopman分析
Koopman analysis in oscillator synchronization
论文作者
论文摘要
同步是耦合非线性系统中重要的动力学现象，近年来已经对其进行了广泛的研究。但是，集中在各个轨道上的分析似乎很难扩展到复杂的系统，而全球统计方法过于粗略。 Koopman操作员技术似乎可以很好地平衡两种方法。在本文中，我们通过从观察到的时间序列中提取重要的特征值和特征功能来扩展到Koopman分析到耦合振荡器同步的研究。重新归一化组的分析旨在在振荡较弱的耦合方面得出本征功能的分析近似。对于中等或强的耦合，数值计算进一步证实了平均频率和相关特征功能的重要性。通过在不同的耦合强度下检查相邻征征的相关性，可以以很高的精度位于同步过渡点，这很容易应用于其他非线性系统。
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global statistical approach is overly cursory. Koopman operator technique seems to well balance the two approaches. In this paper, we extend Koopman analysis to the study of synchronization of coupled oscillators by extracting important eigenvalues and eigenfunctions from the observed time series. A renormalization group analysis is designed to derive an analytic approximation of the eigenfunction in case of weak coupling that dominates the oscillation. For moderate or strong couplings, numerical computation further confirms the importance of the average frequencies and the associated eigenfunctions. The synchronization transition points could be located with quite high accuracy by checking the correlation of neighbouring eigenfunctions at different coupling strengths, which is readily applied to other nonlinear systems.
