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Author: Marwan, Norbert × End date: 2024 × Start date: 2020 × End date: 2024 × Start date: 2020 × Subject: plots ×

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    Recurrence flow measure of nonlinear dependence
    (Berlin ; Heidelberg : Springer, 2022) Braun, Tobias; Kraemer, K. Hauke; Marwan, Norbert
    Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm.
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    Averaged recurrence quantification analysis: Method omitting the recurrence threshold choice
    (Berlin ; Heidelberg : Springer, 2022) Pánis, Radim; Adámek, Karel; Marwan, Norbert
    Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work, we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal-to-noise ratios of lengths 10 2, 10 3, 10 4, and 10 5. To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).