### Abstract

The applicability of the Grassberger-Procaccia (GP) algorithm for estimating the correlation dimension of the chaotic saddle from an ensemble of transient chaotic time series is demonstrated. A numerical procedure is given with an example of the Hènon map to find the rates of separation of neighboring phase-space states constructed from each transient time series in an ensemble to extract Lyapunov exponents. It is also shown that unstable periodic orbits of low period can be detected reliably from an ensemble of transient chaotic time series by using the LK algorithm.

Original language | English (US) |
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Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 64 |

Issue number | 5 II |

State | Published - Nov 2001 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Analyses of transient chaotic time series.** / Dhamala, M.; Lai, Ying-Cheng; Kostelich, Eric.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 64, no. 5 II.

}

TY - JOUR

T1 - Analyses of transient chaotic time series

AU - Dhamala, M.

AU - Lai, Ying-Cheng

AU - Kostelich, Eric

PY - 2001/11

Y1 - 2001/11

N2 - The applicability of the Grassberger-Procaccia (GP) algorithm for estimating the correlation dimension of the chaotic saddle from an ensemble of transient chaotic time series is demonstrated. A numerical procedure is given with an example of the Hènon map to find the rates of separation of neighboring phase-space states constructed from each transient time series in an ensemble to extract Lyapunov exponents. It is also shown that unstable periodic orbits of low period can be detected reliably from an ensemble of transient chaotic time series by using the LK algorithm.

AB - The applicability of the Grassberger-Procaccia (GP) algorithm for estimating the correlation dimension of the chaotic saddle from an ensemble of transient chaotic time series is demonstrated. A numerical procedure is given with an example of the Hènon map to find the rates of separation of neighboring phase-space states constructed from each transient time series in an ensemble to extract Lyapunov exponents. It is also shown that unstable periodic orbits of low period can be detected reliably from an ensemble of transient chaotic time series by using the LK algorithm.

UR - http://www.scopus.com/inward/record.url?scp=18144446486&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144446486&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144446486

VL - 64

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5 II

ER -