Weighted recurrence network for characterizing continuous dynamical systems

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.