### 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 |
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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

Dhamala, M., Lai, Y. C., Kostelich, E. J., & Lai, Y-C. (2000). Detecting unstable periodic orbits from transient chaotic time series.

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*61*(6), 6485-6489.