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

2002/01/31 by Norbert Marwan, N. Marwan, Niels Wessel +7 · 21 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Nonlinear Dynamics and Pattern Formation #nlin.CD #physics.data-an #physics.med-ph #q-bio.QM

paper · pdf · doi:10.1103/physreve.66.026702

published as Physical Review E, 66(2), 2002, 026702

arxiv created 2002/05/21 · openalex publication_date 2002/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Fractal Geometry of Nature
• Determining Lyapunov exponents from a time series

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