Complex Network from Pseudoperiodic Time Series: Topology versus Dynamics

J. Zhang and M. Small
Phys. Rev. Lett. 96, 238701 – Published 14 June 2006

Abstract

We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series generate networks that exhibit small world and scale free features. We show that this distinction in topological structure results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Standard measures of structure in complex networks can therefore be applied to distinguish different dynamic regimes in time series. Application to human electrocardiograms shows that such statistical properties are able to differentiate between the sinus rhythm cardiograms of healthy volunteers and those of coronary care patients.

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  • Received 14 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.96.238701

©2006 American Physical Society

Authors & Affiliations

J. Zhang and M. Small

  • Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

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Issue

Vol. 96, Iss. 23 — 16 June 2006

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