Recurrence-plot-based measures of complexity and their application to heart-rate-variability data

Norbert Marwan, Niels Wessel, Udo Meyerfeldt, Alexander Schirdewan, and Jürgen Kurths
Phys. Rev. E 66, 026702 – Published 6 August 2002
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Abstract

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

  • Received 7 January 2002

DOI:https://doi.org/10.1103/PhysRevE.66.026702

©2002 American Physical Society

Authors & Affiliations

Norbert Marwan1,*, Niels Wessel1, Udo Meyerfeldt2, Alexander Schirdewan2, and Jürgen Kurths1

  • 1Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany
  • 2Franz-Volhard-Hospital, HELIOS Kliniken Berlin, Charité, Humboldt University Berlin, Wiltbergstrasse 50, 13125 Berlin, Germany

  • *Electronic address: marwan@agnld.uni-potsdam.de

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Vol. 66, Iss. 2 — August 2002

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