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The ordinal Kolmogorov-Sinai entropy: A generalized approximation

J.S. Armand Eyebe Fouda 1, * Wolfram Koepf 2, * Sabir Jacquir 3, *
* Auteur correspondant
1 Département de physique (Faculté des sciences, Université de Yaoundé 1)
2 Institut für Mathematik [Kassel]
3 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]
Abstract : We introduce the multi-dimensional ordinal arrays complexity as a generalized approximation of the ordinal Komogorov-Sinai entropy. The ordinal arrays entropy (OAE) is defined as the Shannon entropy of a series of m-ordinal patterns encoded symbols, while the ordinal arrays complexity (OAC) is defined as the differential of the OAE with respect to m. We theoretically establish that the OAC provides a better estimate of the complexity measure for short length time series. Simulations were carried out using discrete maps, and confirm the efficiency of the OAC as complexity measure from a small data set even in a noisy environment. (C) 2016 Elsevier B.V. All rights reserved.
Keywords : Chaos Discrete Maps Quasi-Periodic Route Permutation Entropy Complexity Entropy Ordinal pattern Ordinal array
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01442696
Contributeur : Le2i - Université de Bourgogne <>
Soumis le : vendredi 20 janvier 2017 - 19:46:16
Dernière modification le : vendredi 17 juillet 2020 - 14:54:10

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J.S. Armand Eyebe Fouda, Wolfram Koepf, Sabir Jacquir. The ordinal Kolmogorov-Sinai entropy: A generalized approximation. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2017, 46, pp.103 - 115. ⟨10.1016/j.cnsns.2016.11.001⟩. ⟨hal-01442696⟩

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