Abstract
We address under what conditions dynamical coupling between chaotic systems can be detected reliably from scalar time series. In particular, we study weakly coupled chaotic systems and focus on the detectability of the correlation dimension of the chaotic invariant set by utilizing the Grassberger-Procaccia algorithm. An algebraic scaling law is obtained, which relates the necessary length of the time series to a key parameter of the system: the coupling strength. The scaling law indicates that an extraordinarily long time series is required for detecting the coupling dynamics.
| Original language | English (US) |
|---|---|
| Article number | 036217 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 66 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2002 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Detectability of dynamical coupling from delay-coordinate embedding of scalar time series. / Lai, Ying-Cheng; Kostelich, Eric.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 66, No. 3, 036217, 09.2002.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Detectability of dynamical coupling from delay-coordinate embedding of scalar time series
AU - Lai, Ying-Cheng
AU - Kostelich, Eric
PY - 2002/9
Y1 - 2002/9
N2 - We address under what conditions dynamical coupling between chaotic systems can be detected reliably from scalar time series. In particular, we study weakly coupled chaotic systems and focus on the detectability of the correlation dimension of the chaotic invariant set by utilizing the Grassberger-Procaccia algorithm. An algebraic scaling law is obtained, which relates the necessary length of the time series to a key parameter of the system: the coupling strength. The scaling law indicates that an extraordinarily long time series is required for detecting the coupling dynamics.
AB - We address under what conditions dynamical coupling between chaotic systems can be detected reliably from scalar time series. In particular, we study weakly coupled chaotic systems and focus on the detectability of the correlation dimension of the chaotic invariant set by utilizing the Grassberger-Procaccia algorithm. An algebraic scaling law is obtained, which relates the necessary length of the time series to a key parameter of the system: the coupling strength. The scaling law indicates that an extraordinarily long time series is required for detecting the coupling dynamics.
UR - http://www.scopus.com/inward/record.url?scp=45849154980&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=45849154980&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.66.036217
DO - 10.1103/PhysRevE.66.036217
M3 - Article
VL - 66
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 3
M1 - 036217
ER -