Journal
PHYSICS LETTERS A
Volume 355, Issue 1, Pages 27-31Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2006.01.093
Keywords
chaotic maps; order patterns; permutation entropy; discrete Lyapunov exponent; chaotic cryptography
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Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on 'forbidden' order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed. (c) 2006 Elsevier B.V. All rights reserved.
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