Recurrence Plots and Cross Recurrence Plots

Nonlinear Analysis, 13(2), 947–952p. (2012) DOI:10.1016/j.nonrwa.2011.08.029

A directed weighted complex network for characterizing chaotic dynamics from time series

We propose a reliable method for constructing a directed weighted complex network (DWCN) from a time series. Through investigating the DWCN for various time series, we find that time series with different dynamics exhibit distinct topological properties. We indicate this topological distinction results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Furthermore, we associate different aspects of dynamics with the topological indices of the DWCN, and illustrate how the DWCN can be exploited to detect unstable periodic orbits of different periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach.