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.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - Nov 2001
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics