Entropy of weighted recurrence plots

Deniz Eroglu, Thomas K. DM. Peron, Nobert Marwan, Francisco A. Rodrigues, Francisco A. Rodrigues, Michael Sebek, Istvan Z. Kiss, Jurgen Kurths

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.
Original languageEnglish
Article number042919
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume90
Issue number4
DOIs
Publication statusPublished - Oct 2014

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Recurrence Plot
Shannon Entropy
Recurrence
plots
Entropy
Recurrence Quantification Analysis
entropy
Largest Lyapunov Exponent
Inconsistent
Quantify
Time series
Experimental Data
Alternatives
exponents
Demonstrate
Experiment
Standards

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Eroglu, D., Peron, T. K. DM., Marwan, N., Rodrigues, F. A., Rodrigues, F. A., Sebek, M., ... Kurths, J. (2014). Entropy of weighted recurrence plots. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, 90(4), [042919]. https://doi.org/10.1103/PhysRevE.90.042919

Entropy of weighted recurrence plots. / Eroglu, Deniz; Peron, Thomas K. DM.; Marwan, Nobert; Rodrigues, Francisco A.; Rodrigues, Francisco A.; Sebek, Michael; Kiss, Istvan Z. ; Kurths, Jurgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 90, No. 4, 042919, 10.2014.

Research output: Contribution to journalArticle

Eroglu, D, Peron, TKDM, Marwan, N, Rodrigues, FA, Rodrigues, FA, Sebek, M, Kiss, IZ & Kurths, J 2014, 'Entropy of weighted recurrence plots', Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 90, no. 4, 042919. https://doi.org/10.1103/PhysRevE.90.042919
Eroglu D, Peron TKDM, Marwan N, Rodrigues FA, Rodrigues FA, Sebek M et al. Entropy of weighted recurrence plots. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2014 Oct;90(4). 042919. https://doi.org/10.1103/PhysRevE.90.042919
Eroglu, Deniz ; Peron, Thomas K. DM. ; Marwan, Nobert ; Rodrigues, Francisco A. ; Rodrigues, Francisco A. ; Sebek, Michael ; Kiss, Istvan Z. ; Kurths, Jurgen. / Entropy of weighted recurrence plots. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2014 ; Vol. 90, No. 4.
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