School of Electrical Engineering and Automation, Tianjin University, Tianjin, People's Republic of China.
Chaos. 2009 Sep;19(3):033137. doi: 10.1063/1.3227736.
We propose in this paper a reliable method for constructing complex networks from a time series with each vector point of the reconstructed phase space represented by a single node and edge determined by the phase space distance. Through investigating an extensive range of network topology statistics, we find that the constructed network inherits the main properties of the time series in its structure. Specifically, periodic series and noisy series convert into regular networks and random networks, respectively, and networks generated from chaotic series typically exhibit small-world and scale-free features. Furthermore, we associate different aspects of the dynamics of the time series with the topological indices of the network and demonstrate how such statistics can be used to distinguish different dynamical regimes. Through analyzing the chaotic time series corrupted by measurement noise, we also indicate the good antinoise ability of our method.
本文提出了一种可靠的方法，可通过将重构相空间中的每个向量点表示为单个节点，并通过相空间距离确定边，从时间序列中构建复杂网络。通过研究广泛的网络拓扑统计数据，我们发现所构建的网络在其结构中继承了时间序列的主要性质。具体来说，周期性序列和噪声序列分别转化为规则网络和随机网络，而来自混沌序列的网络通常表现出小世界和无标度特征。此外，我们将时间序列动力学的不同方面与网络的拓扑指标联系起来，并展示了如何使用这些统计数据来区分不同的动力学状态。通过分析受测量噪声干扰的混沌时间序列，我们还表明了我们的方法具有良好的抗噪能力。
