Recurrence Plots 25 years later -- gaining confidence in dynamical transitions

Abstract

Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.

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• A Punctuated Equilibrium Analysis of the Climate Evolution of Cenozoic exhibits a Hierarchy of Abrupt Transitions
• Sampling rate-corrected analysis of irregularly sampled time series
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• Recurrence quantification analysis as a post-processing technique in adaptive optics high-contrast imaging
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• Optimising Parameters in Recurrence Quantification Analysis of Smart Energy Systems