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Sampling period, statistical complexity, and chaotic attractors

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  • De Micco, Luciana
  • Fernández, Juana Graciela
  • Larrondo, Hilda A.
  • Plastino, Angelo
  • Rosso, Osvaldo A.

Abstract

We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling periodtM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period τ. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens’ one in a delay-time embedding, on one hand, and the exact Nyquist–Shannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens’ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension 2

Suggested Citation

  • De Micco, Luciana & Fernández, Juana Graciela & Larrondo, Hilda A. & Plastino, Angelo & Rosso, Osvaldo A., 2012. "Sampling period, statistical complexity, and chaotic attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2564-2575.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:8:p:2564-2575
    DOI: 10.1016/j.physa.2011.12.042
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    1. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.
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    4. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.
    5. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
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    1. He, Shaobo & Sun, Kehui & Wang, Huihai, 2016. "Multivariate permutation entropy and its application for complexity analysis of chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 812-823.
    2. Chrisment, Antoine M. & Firpo, Marie-Christine, 2016. "Entropy–complexity analysis in some globally-coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 162-173.
    3. De Micco, L. & Antonelli, M. & Larrondo, H.A., 2017. "Stochastic degradation of the fixed-point version of 2D-chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 477-484.

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