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The European Physical Journal B, 2013, 86:116.
Osvaldo A. Rosso, Felipe Olivares, Luciano Zunino, Luciana De Micco, André L. L. Aquino, Angelo Plastino, Hilda A. Larrondo.
1116. LaCCAN/CPMAT – Instituto de Computação, Universidade Federal de Alagoas, BR 104 Norte km 97 57072-970, Maceió, Alagoas, Brazil and
2116. Laboratorio de Sistemas Complejos, Facultad de Ingeniería, Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires, Argentina and
3116. Fellow of CONICET-Argentina, 1033 Av. Rivadavia 1917, Ciudad Autónoma de Buenos Aires, Argentina and
4116. Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), C.C. 67, 1900, La Plata, Argentina and
5116. Centro de Investigaciones Ópticas, CIOp (CONICET La Plata – CIC), C.C. 3, 1897, Gonnet, Argentina and
6116. Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900, La Plata, Argentina and
7116. 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 and
8116. Instituto de Física, IFLP-CCT, Universidad Nacional de La Plata (UNLP), C.C. 727, 1900, La Plata, Argentina and
9116. Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
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 forD < 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.
