Detectability of dynamical coupling from delay-coordinate embedding of scalar time series

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4 Citations (Scopus)

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 languageEnglish (US)
Article number036217
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number3
DOIs
StatePublished - Sep 2002

Fingerprint

Detectability
embedding
Time series
Scalar
Scaling Laws
scalars
scaling laws
Chaotic System
Correlation Dimension
Invariant Set
Coupled System
Necessary

ASJC Scopus subject areas

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

Cite this

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title = "Detectability of dynamical coupling from delay-coordinate embedding of scalar time series",
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.",
author = "Ying-Cheng Lai and Eric Kostelich",
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