https://doi.org/10.1140/epjb/e2013-30764-5
Regular Article
Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution
1 LaCCAN/CPMAT – Instituto de
Computação, Universidade Federal de Alagoas, BR 104 Norte km 97 57072-970, Maceió, Alagoas, Brazil
2 Laboratorio de Sistemas Complejos,
Facultad de Ingeniería, Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires,
Argentina
3 Fellow of CONICET-Argentina, 1033 Av.
Rivadavia 1917, Ciudad Autónoma de
Buenos Aires, Argentina
4 Departamento de Física, Facultad de
Ciencias Exactas, Universidad Nacional de La Plata (UNLP),
C.C. 67, 1900
La Plata,
Argentina
5 Centro de Investigaciones Ópticas,
CIOp (CONICET La Plata - CIC), C.C. 3, 1897
Gonnet,
Argentina
6 Departamento de Ciencias Básicas,
Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP),
1900
La Plata,
Argentina
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
8 Instituto de Física, IFLP-CCT,
Universidad Nacional de La Plata (UNLP), C.C. 727, 1900
La Plata,
Argentina
9 Instituto de Física Interdisciplinar
y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes
Balears, E-07122
Palma de Mallorca,
Spain
a
e-mail: oarosso@gmail.com
Received:
21
August
2012
Received in final form:
17
December
2012
Published online:
27
March
2013
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 Dmin-value such that forbidden patterns cannot appear for D < Dmin. 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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013
