### Abstract

We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of finding periodic orbits from transient chaotic time series and derive a scaling law for this probability. The scaling law implies that unstable periodic orbits of high periods are practically undetectable from transient chaos.

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

Pages (from-to) | 6485-6489 |

Number of pages | 5 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 61 |

Issue number | 6 |

Publication status | Published - Jun 2000 |

### Keywords

- STRANGE ATTRACTORS
- VORTEX PAIRS
- SYSTEMS
- SADDLES
- DIMENSIONS
- ADVECTION
- FLOWS
- BOUNDARIES
- REPELLERS
- POINTS

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*61*(6), 6485-6489.

**Detecting unstable periodic orbits from transient chaotic time series.** / Dhamala, M ; Lai, Y C ; Kostelich, E J ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 61, no. 6, pp. 6485-6489.

}

TY - JOUR

T1 - Detecting unstable periodic orbits from transient chaotic time series

AU - Dhamala, M

AU - Lai, Y C

AU - Kostelich, E J

AU - Lai, Ying-Cheng

PY - 2000/6

Y1 - 2000/6

N2 - We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of finding periodic orbits from transient chaotic time series and derive a scaling law for this probability. The scaling law implies that unstable periodic orbits of high periods are practically undetectable from transient chaos.

AB - We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of finding periodic orbits from transient chaotic time series and derive a scaling law for this probability. The scaling law implies that unstable periodic orbits of high periods are practically undetectable from transient chaos.

KW - STRANGE ATTRACTORS

KW - VORTEX PAIRS

KW - SYSTEMS

KW - SADDLES

KW - DIMENSIONS

KW - ADVECTION

KW - FLOWS

KW - BOUNDARIES

KW - REPELLERS

KW - POINTS

M3 - Article

VL - 61

SP - 6485

EP - 6489

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

ER -