Multiscale characterization of recurrence-based phase space networks constructed from time series

TL;DR

This paper explores multiscale analysis of recurrence-based phase space networks derived from time series, revealing how network properties reflect underlying dynamical behaviors across different scales.

Contribution

It introduces a systematic investigation of recurrence-based phase space networks, highlighting their multiscale topological features and relation to dynamical system types.

Findings

Network size scales with different exponents for various dynamics.

Degree distribution is bell-shaped around 2k with varying variance.

Local network metrics relate to orbit stability and provide complementary insights.

Abstract

Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network theory provides a tool to describe either important nodes, or structures that exist in the networks, at different topological scale. This can then provide distinct information for time series of different dynamical systems. In this paper, we systematically investigate the recurrence-based phase space network of order $k$ that has previously been used to specify different types of dynamics in terms of the motif ranking from a different perspective. Globally, we find that the network size scales with different scale exponents and the degree distribution follows a quasi-symmetric bell shape around the value of $2k$ with different values of degree variance from periodic to chaotic R\"{o}ssler systems. Local network properties such as the vertex degree, the clustering coefficients and betweenness centrality are found to be sensitive to the local stability of the orbits and hence contain complementary information.