在复杂系统中,事件以不规则的时间间隔发生,这些间隔本质上编码了系统的内在动力学。分析事件的时间聚类能够揭示非随机模式及时间演化特征。现有技术可通过全局统计量有效量化事件的整体聚类倾向,但这些宏观方法存在关键缺陷:未能深入探究单个聚类的动力学特性。分析单个聚类至关重要,因为它有助于理解主动驱动系统动态的局部相互作用,而这些作用可能被全局平均所掩盖,同时还能揭示涉及的时间尺度。为解决上述局限性,我们提出一种基于复杂网络的框架,用于分析不规则时间间隔下事件的聚类行为。该框架利用到达时间建立连接,将时间序列转化为网络结构,并通过网络属性量化聚类特征。此外,采用社区检测算法识别时间序列中的个体聚类。我们通过标准到达过程(如泊松过程和马尔可夫调制泊松过程)验证该方法的有效性。为进一步展示其适用范围,我们将该方法应用于两类不同系统:湍流中液滴到达的时间序列以及心电图(ECG)信号中的R-R间期序列。
In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal evolution. Existing techniques can effectively quantify the overall clustering tendency of events using global statistical measures. However, these macroscopic approaches leave a critical gap, as they do not attempt to investigate the dynamics of individual clusters. Analyzing individual clusters is essential, as it helps comprehend the local interactions that actively drive the system dynamics, which may be obscured by global averaging, while simultaneously revealing the time scales involved. To address these limitations, we propose a complex network-based framework for analyzing clustering of events occurring at irregular intervals. The framework establishes connections using arrival times, transforming the time series into a network. Network properties are then used to quantify the clustering. Further, a community detection algorithm is used to identify individual clusters in time series. We illustrate the method by applying it to standard arrival processes, such as the Poisson process and the Markov-modulated Poisson process. To further demonstrate its scope, we apply the method to two diverse systems: the time series of droplet arrivals in turbulent flows and the R-R intervals in electrocardiogram (ECG) signals.