arXiv 2009.092272020-09-19nlin.CD

振荡器同步中的Koopman分析

Koopman analysis in oscillator synchronization

Jing Hu, Yueheng Lan

发表信息：: Phys. Rev. E 102, 062216 (2020)
DOI：: 10.1103/PhysRevE.102.062216

摘要：

同步是耦合非线性系统中一种重要的动力学现象，近年来得到了广泛的研究。然而，集中于单个轨道的分析似乎很难扩展到复杂系统，而全局统计方法过于粗略。库普曼算子技术似乎很好地平衡了这两种方法。本文将Koopman分析推广到耦合振子同步的研究中，从观测的时间序列中提取重要的特征值和特征函数。一个重整化群分析的目的是推导出一个解析近似的本征函数的情况下，弱耦合，占主导地位的振荡。对于中等或强耦合，数值计算进一步证实了平均频率和相关的本征函数的重要性。通过检测不同耦合强度下相邻本征函数的相关性，可以很高精度地定位同步跃迁点，该方法也适用于其它非线性系统。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文