Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data
Abstract
In complex systems the knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the processes going on there. Linear approaches are often not sufficient to describe these processes and several nonlinear methods 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 to detect transitions between chaotic and periodic states, as well as to identify additional laminar states, i.e. chaos-chaos transitions. Traditional recurrence quantification analysis fails to detect these latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify laminar phases before a life-threatening cardiac arrhythmia and, thus, to enable a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.Keywords
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