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2017 ; 7
(1
): 1087
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How to test for partially predictable chaos
#MMPMID28439074
Wernecke H
; Sándor B
; Gros C
Sci Rep
2017[Apr]; 7
(1
): 1087
PMID28439074
show ga
For a chaotic system pairs of initially close-by trajectories become eventually
fully uncorrelated on the attracting set. This process of decorrelation can split
into an initial exponential decrease and a subsequent diffusive process on the
chaotic attractor causing the final loss of predictability. Both processes can be
either of the same or of very different time scales. In the latter case the two
trajectories linger within a finite but small distance (with respect to the
overall extent of the attractor) for exceedingly long times and remain partially
predictable. Standard tests for chaos widely use inter-orbital correlations as an
indicator. However, testing partially predictable chaos yields mostly ambiguous
results, as this type of chaos is characterized by attractors of fractally
broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos
based on the cross-distance scaling of pairs of initially close trajectories.
This test robustly discriminates chaos, including partially predictable chaos,
from laminar flow. Additionally using the finite time cross-correlation of pairs
of initially close trajectories, we are able to identify laminar flow as well as
strong and partially predictable chaos in a 0-1 manner solely from the properties
of pairs of trajectories.
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