True and false forbidden patterns in deterministic and random dynamics

J. M. Amigó, S. Zambrano, M. A F Sanjún

Research output: Contribution to journalArticle

94 Citations (Scopus)

Abstract

In this letter we discuss some properties of order patterns both in deterministic and random orbit generation. As it turns out, the orbits of one-dimensional maps have always forbidden patterns, i.e., order patterns that cannot occur, in contrast with random time series, in which any order pattern appears with probability one. However, finite random sequences may exhibit "false" forbidden patterns with non-vanishing probability. In this case, forbidden patterns decay with the sequence length, thus unveiling the random nature of the sequence. Last but not least, true forbidden patterns are robust against noise and disintegrate with a rate that depends on the noise level. These properties can be embodied in a simple method to distinguish deterministic, finite time series with very high levels of observational noise, from random ones. We present numerical evidence for white noise.

Original languageEnglish
Article number50001
JournalEPL
Volume79
Issue number5
DOIs
Publication statusPublished - Sep 1 2007

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orbits
white noise
decay

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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True and false forbidden patterns in deterministic and random dynamics. / Amigó, J. M.; Zambrano, S.; Sanjún, M. A F.

In: EPL, Vol. 79, No. 5, 50001, 01.09.2007.

Research output: Contribution to journalArticle

Amigó, J. M. ; Zambrano, S. ; Sanjún, M. A F. / True and false forbidden patterns in deterministic and random dynamics. In: EPL. 2007 ; Vol. 79, No. 5.
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