基于递归的时间序列相空间网络的多尺度特征
Multiscale characterization of recurrence-based phase space networks constructed from time series
摘要：
近年来，通过构造关联复杂网络来分析时间序列的框架引起了人们极大的研究兴趣。复杂网络方法研究时间序列的一个优点是，复杂网络理论提供了一种工具，可以在不同的拓扑尺度上描述网络中存在的重要节点或结构。这可以为不同动力系统的时间序列提供不同的信息。在本文中，我们系统地研究了递归为基础的相空间网络的顺序$k$，以前已被用来指定不同类型的动态的主题排名从不同的角度来看。在全局范围内，我们发现从周期到混沌的Rössler系统，网络的规模具有不同的标度指数，度分布在$2k$值附近具有不同的度方差值.局部网络属性，如顶点度，聚类系数和介数中心性被发现是敏感的局部稳定性的轨道，因此包含互补信息。
英文摘要：
Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network theory provides a tool to describe either important nodes, or structures that exist in the networks, at different topological scale. This can then provide distinct information for time series of different dynamical systems. In this paper, we systematically investigate the recurrence-based phase space network of order $k$ that has previously been used to specify different types of dynamics in terms of the motif ranking from a different perspective. Globally, we find that the network size scales with different scale exponents and the degree distribution follows a quasi-symmetric bell shape around the value of $2k$ with different values of degree variance from periodic to chaotic Rössler systems. Local network properties such as the vertex degree, the clustering coefficients and betweenness centrality are found to be sensitive to the local stability of the orbits and hence contain complementary information.
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