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

TLDR

Understanding transitions among regular, laminar, and chaotic dynamics is crucial for complex systems, yet linear methods are often inadequate and nonlinear techniques typically require long data records. The authors aim to introduce recurrence‑plot‑based complexity measures that rely on vertical structures and apply them to the logistic map and heart‑rate‑variability data. They compute vertical‑structure metrics from recurrence plots of the logistic map and HRV time series to quantify complexity. These metrics detect chaotic‑periodic and laminar‑state transitions in the logistic map, outperform traditional recurrence quantification analysis, and identify laminar phases preceding life‑threatening arrhythmias, offering potential for early arrhythmia prediction and therapy.

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.