Order patterns and chaos |
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Institution: | 1. Centro de Investigación Operativa, Universidad Miguel Hernández, E-03202 Elche, Spain;2. Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402, USA;3. Institute for Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, PL-00-049 Warsaw, Poland |
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Abstract: | 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. |
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