TY - JOUR
T1 - Detectability of dynamical coupling from delay-coordinate embedding of scalar time series
AU - Lai, Ying-Cheng
AU - Kostelich, Eric
PY - 2002/9/24
Y1 - 2002/9/24
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.
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U2 - 10.1103/PhysRevE.66.036217
DO - 10.1103/PhysRevE.66.036217
M3 - Article
C2 - 12366234
AN - SCOPUS:45849154980
SN - 1063-651X
VL - 66
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -