Recurrence network (RN) is a powerful tool for the analysis of complex dynamical systems. It integrates complex network theory with the idea of recurrence of a trajectory, i.e. whether two state vectors are close neighbors in a phase space. However, the differences in proximity between connected state vectors are not considered in the RN construction. Here, we propose a weighted state vector recurrence network method which assigns weights to network links based on the proximity of the two connected state vectors. On the basis, we further propose a weighted data segment recurrence network that takes continuous data segments as nodes for the analysis of noisy time series. The feasibility of the proposed methods is illustrated based on the Lorenz system. Finally, an application to five types of EEG recordings is conducted to demonstrate the potentials of the proposed methods in the study of real-world data.

中文翻译：

---

用于表征连续动力系统的加权递归网络

递归网络（RN）是分析复杂动力系统的强大工具。它将复杂网络理论与轨迹递归的思想相结合，即两个状态向量在相空间中是否是近邻。然而，在 RN 构造中没有考虑连接状态向量之间的接近度差异。在这里，我们提出了一种加权状态向量递归网络方法，该方法根据两个连接状态向量的接近程度为网络链接分配权重。在此基础上，我们进一步提出了一种以连续数据段为节点的加权数据段递归网络，用于噪声时间序列的分析。基于洛伦兹系统说明了所提出方法的可行性。最后，