- ...Republic
- Present
address, e-mail: mp@uivt.cas.cz,
mp@santafe.edu.
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- ...variance
- Note, that the GPER (3)
is variance-dependent. Therefore all analyzed
time series were rescaled to have unit variance
so that
the GPER should classify the series according to their
dynamics, without the influence of the variance.
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- ...periodograms
- I.e., discrete estimates of
the spectral density obtained as
squared magnitudes of the Fourier coefficients.
The integral in (3) is then computed as
a sum over the 8192 periodogram bins.
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- ...shifted
- This shift is equivalent to
an addition of white noise to the original
time series and thus it could worsen distinction of system
states with similar spectra. On the other hand, presence
of a few periodogram bins with magnitude close to zero
could bias the GPER estimate downwards and obscure
the dependence of GPER on a system parameter.
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- ...paper.
- Stability of GPER
estimates obtained
from shorter time series or from individual
realizations
and other technical questions
will be discussed elsewhere.
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- ...value
- Strictly speaking, the GPER is not
defined for periodic states, and its formally estimated
values do not reflect behaviour of negative LE
- see Fig. 5.
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- ...KSE/LE?
- The author
is grateful to an anonymous referee for posing
this interesting question.
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- ...thousand
- Hundred thousand initial iterations
were skipped as transient time also in all numerical studies
presented in previous section.
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- ...three
- Equivalent results have also been obtained
from tent, tilted tent, Gaussian and Hénon
maps [27].
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