Complex network analysis of recurrences in phase space

Norbert Marwan(1), Reik Donner(1), Jonathan Donges(1), Yong Zou(2), Jürgen Kurths(1)
(1) Potsdam Institute for Climate Impact Research
(2) The Hong Kong Polytechnic University

Short Abstract

During the last years, increasing efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant statistical properties of time series. We present a novel approach for analysing time series using complex network theory. Starting from the concept of recurrences in phase space, we identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network, thus linking different points in time if the considered states are closely neighboured in phase space.

We demonstrate that fundamental relationships between topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system exist. This novel interpretation of the recurrence matrix provides new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) and, thus, complementary information about structural features of dynamical systems that substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) methods.

An application from palaeo-climate illustrates the potential of the new approach.