### Abstract

Original language | English |
---|---|

Article number | 144101 |

Journal | Physical Review Letters |

Volume | 118 |

Issue number | 4 |

DOIs | |

Publication status | Published - 7 Apr 2017 |

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### Cite this

**Quantifying the Dynamical Complexity of Chaotic Time Series.** / Politi, Antonio.

Research output: Contribution to journal › Letter

*Physical Review Letters*, vol. 118, no. 4, 144101. https://doi.org/10.1103/PhysRevLett.118.144101

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TY - JOUR

T1 - Quantifying the Dynamical Complexity of Chaotic Time Series

AU - Politi, Antonio

N1 - Acknowledgements The author wishes to acknowledge G. Giacomelli, M. Mulansky, and L. Ricci for early discussions.

PY - 2017/4/7

Y1 - 2017/4/7

N2 - A powerful approach is proposed for the characterization of chaotic signals. It is based on the combined use of two classes of indicators: (i) the probability of suitable symbolic sequences (obtained from the ordinal patterns of the corresponding time series); (ii) the width of the corresponding cylinder sets. This way, much information can be extracted and used to quantify the complexity of a given signal. As an example of the potentiality of the method, I introduce a modified permutation entropy which allows for quantitative estimates of the Kolmogorov-Sinai entropy in hyperchaotic models, where other methods would be unpractical. As a by-product, estimates of the fractal dimension of the underlying attractors are possible as well.

AB - A powerful approach is proposed for the characterization of chaotic signals. It is based on the combined use of two classes of indicators: (i) the probability of suitable symbolic sequences (obtained from the ordinal patterns of the corresponding time series); (ii) the width of the corresponding cylinder sets. This way, much information can be extracted and used to quantify the complexity of a given signal. As an example of the potentiality of the method, I introduce a modified permutation entropy which allows for quantitative estimates of the Kolmogorov-Sinai entropy in hyperchaotic models, where other methods would be unpractical. As a by-product, estimates of the fractal dimension of the underlying attractors are possible as well.

U2 - 10.1103/PhysRevLett.118.144101

DO - 10.1103/PhysRevLett.118.144101

M3 - Letter

VL - 118

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 4

M1 - 144101

ER -