### Abstract

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (C) 1998 American Institute of Physics. [S1054-1500(98)00904-5].

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

Pages (from-to) | 853-860 |

Number of pages | 8 |

Journal | Chaos |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1998 |

### Keywords

- low-dimensional dynamics
- time-series
- strange sets
- topological analysis
- plateau onset
- attractors
- biology
- occur
- laws

### Cite this

*Chaos*,

*8*(4), 853-860. https://doi.org/10.1063/1.166371

**Counting unstable periodic orbits in noisy chaotic systems : A scaling relation connecting experiment with theory.** / Pei, Xing; Dolan, Kevin; Moss, Frank; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Chaos*, vol. 8, no. 4, pp. 853-860. https://doi.org/10.1063/1.166371

}

TY - JOUR

T1 - Counting unstable periodic orbits in noisy chaotic systems

T2 - A scaling relation connecting experiment with theory

AU - Pei, Xing

AU - Dolan, Kevin

AU - Moss, Frank

AU - Lai, Ying-Cheng

PY - 1998/12

Y1 - 1998/12

N2 - The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (C) 1998 American Institute of Physics. [S1054-1500(98)00904-5].

AB - The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (C) 1998 American Institute of Physics. [S1054-1500(98)00904-5].

KW - low-dimensional dynamics

KW - time-series

KW - strange sets

KW - topological analysis

KW - plateau onset

KW - attractors

KW - biology

KW - occur

KW - laws

U2 - 10.1063/1.166371

DO - 10.1063/1.166371

M3 - Article

VL - 8

SP - 853

EP - 860

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 4

ER -