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Contrasting stochasticity with chaos in a permutation Lempel–Ziv complexity — Shannon entropy plane

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  • Mateos, Diego M.
  • Zozor, Steeve
  • Olivares, Felipe

Abstract

This paper aims at introducing the Lempel–Ziv permutation complexity vs. permutation entropy plane (EC-plane) as a tool to analyze time series with diverse dynamical nature. These two quantities use the Bandt and Pompe representation to quantify a continuous-state time series. The main strength of this approach lies in the fact that this plane combines two different perspectives to study a signal, one being purely statistic (the permutation entropy) and the other being algorithmic (the Lempel–Ziv complexity). The results allow us to conclude that the EC-plane constitutes an appropriate framework for: (i) characterizing non-linear chaotic maps, (ii) distinguishing deterministic from stochastic processes and (iii) to discriminate between fractional Brownian motion, fractional Gaussian noise and K-noise.

Suggested Citation

  • Mateos, Diego M. & Zozor, Steeve & Olivares, Felipe, 2020. "Contrasting stochasticity with chaos in a permutation Lempel–Ziv complexity — Shannon entropy plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120303125
    DOI: 10.1016/j.physa.2020.124640
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    References listed on IDEAS

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    Cited by:

    1. Mateos, Diego M. & Gómez-Ramírez, Jaime & Rosso, Osvaldo A., 2021. "Using time causal quantifiers to characterize sleep stages," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Šapina, Matej & Karmakar, Chandan Kumar & Kramarić, Karolina & Kośmider, Marcin & Garcin, Matthieu & Brdarić, Dario & Milas, Krešimir & Yearwood, John, 2021. "Lempel-Ziv complexity of the pNNx statistics – an application to neonatal stress," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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    Keywords

    Chaos; Noises; Entropy; Complexity; FBM; FGN;
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