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

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 Rössler 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.

Non-final version of Chaos paper

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• The Geometry of Chaotic Dynamics -- A Complex Network Perspective
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Cited by in corpus (6)

• Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
• Analytical framework for recurrence-network analysis of time series
• Time Series Analysis via Network Science: Concepts and Algorithms
• Phase space reconstruction for non-uniformly sampled noisy time series
• Scale-free networks emerging from multifractal time series
• Exploration of period-doubling cascade route to chaos with complex network based time series construction