Recurrence networks - A novel paradigm for nonlinear time series analysis

TL;DR

This paper introduces recurrence networks, a new method transforming time series into complex networks based on phase space recurrences, providing novel insights into the system's dynamical complexity.

Contribution

It presents a unifying framework linking recurrence analysis with complex network theory, revealing fundamental relationships and new quantitative measures of dynamical complexity.

Findings

Recurrence networks relate topological properties to phase space density.

The approach offers new quantitative measures of dynamical complexity.

It unifies existing recurrence analysis methods within a network framework.

Abstract

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis.