空间扩展动力系统中相同步簇的识别
Identifying phase synchronization clusters in spatially extended dynamical systems
摘要：
我们研究了两个最近提出的多变量时间序列分析技术，旨在检测相位同步集群在空间上扩展，非平稳系统方面的现场应用。这两种技术的出发点是一个矩阵，其条目是时间序列对之间测量的平均相位相干值。第一种方法是一个平均场的方法，它允许定义一个子系统在一个单一的同步集群的参与强度。第二种方法是基于一个特征值分解的参与指数，从该指数的特征在于参与程度的子系统内的多个同步集群。模拟耦合洛伦兹振荡器的晶格内的多个集群，我们探索这两种方法的局限性和陷阱，并证明（a）平均场的方法是相对稳健的，即使在配置中的单集群假设不完全满足，和（b）的特征值分解方法正确识别模拟集群，即使是低耦合强度。使用的特征值分解的方法，我们研究了时空同步集群在长期持久的多通道脑电图记录癫痫患者，并获得的结果，充分证实了既定的神经生理学检查技术的结果。多变量时间序列分析方法，如同步聚类分析，占数据中的非线性，预计将提供互补的信息，允许获得更深入的了解空间扩展的复杂系统的集体动态。
英文摘要：
We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems.
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