### 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 language | English |
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Article number | 50001 |

Journal | EPL |

Volume | 79 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 1 2007 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*EPL*,

*79*(5), [50001]. https://doi.org/10.1209/0295-5075/79/50001

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

Research output: Contribution to journal › Article

*EPL*, vol. 79, no. 5, 50001. https://doi.org/10.1209/0295-5075/79/50001

}

TY - JOUR

T1 - True and false forbidden patterns in deterministic and random dynamics

AU - Amigó, J. M.

AU - Zambrano, S.

AU - Sanjún, M. A F

PY - 2007/9/1

Y1 - 2007/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79051468958&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79051468958&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/79/50001

DO - 10.1209/0295-5075/79/50001

M3 - Article

AN - SCOPUS:79051468958

VL - 79

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 5

M1 - 50001

ER -