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Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution

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Abstract

By appealing to a long list of different nonlinear maps we review the characterization of time series arising from chaotic maps. The main tool for this characterization is the permutation Bandt-Pompe probability distribution function. We focus attention on both local and global characteristics of the components of this probability distribution function. We show that forbidden ordinal patterns (local quantifiers) exhibit an exponential growth for pattern-length range 3 ≤ D ≤ 8, in the case of finite time series data. Indeed, there is a minimum D min-value such that forbidden patterns cannot appear for D < D min. The system’s localization in an entropy-complexity plane (global quantifier) displays typical specific features associated with its dynamics’ nature. We conclude that a more “robust” distinction between deterministic and stochastic dynamics is achieved via the present time series’ treatment based on the global characteristics of the permutation Bandt-Pompe probability distribution function.

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Authors and Affiliations

  1. LaCCAN/CPMAT – Instituto de Computação, Universidade Federal de Alagoas, BR 104 Norte km 97 57072-970, Maceió, Alagoas, Brazil

    Osvaldo A. Rosso, Felipe Olivares & André L. L. Aquino

  2. Laboratorio de Sistemas Complejos, Facultad de Ingeniería, Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires, Argentina

    Osvaldo A. Rosso

  3. Fellow of CONICET-Argentina, 1033 Av. Rivadavia 1917, Ciudad Autónoma de Buenos Aires, Argentina

    Osvaldo A. Rosso, Luciano Zunino, Luciana De Micco, Angelo Plastino & Hilda A. Larrondo

  4. Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), C.C. 67, 1900, La Plata, Argentina

    Felipe Olivares

  5. Centro de Investigaciones Ópticas, CIOp (CONICET La Plata - CIC), C.C. 3, 1897, Gonnet, Argentina

    Luciano Zunino

  6. Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900, La Plata, Argentina

    Luciano Zunino

  7. Departamentos de Física y de Ingeniería Electrónica, Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Av. Juan B. Justo 4302, 7600, Mar del Plata, Argentina

    Luciana De Micco & Hilda A. Larrondo

  8. Instituto de Física, IFLP-CCT, Universidad Nacional de La Plata (UNLP), C.C. 727, 1900, La Plata, Argentina

    Angelo Plastino

  9. Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain

    Angelo Plastino

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  1. Osvaldo A. Rosso
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  2. Felipe Olivares
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  4. Luciana De Micco
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  7. Hilda A. Larrondo
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Correspondence to Osvaldo A. Rosso.

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Rosso, O.A., Olivares, F., Zunino, L. et al. Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution. Eur. Phys. J. B 86, 116 (2013). https://doi.org/10.1140/epjb/e2013-30764-5

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