842 research outputs found
Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions
We study how the presence of correlations in physical variables contributes
to the form of probability distributions. We investigate a process with
correlations in the variance generated by (i) a Gaussian or (ii) a truncated
L\'{e}vy distribution. For both (i) and (ii), we find that due to the
correlations in the variance, the process ``dynamically'' generates power-law
tails in the distributions, whose exponents can be controlled through the way
the correlations in the variance are introduced. For (ii), we find that the
process can extend a truncated distribution {\it beyond the truncation cutoff},
which leads to a crossover between a L\'{e}vy stable power law and the present
``dynamically-generated'' power law. We show that the process can explain the
crossover behavior recently observed in the S&P500 stock index.Comment: 7 pages, five figures. To appear in Europhysics Letters (2000
Spurious detection of phase synchronization in coupled nonlinear oscillators
Coupled nonlinear systems under certain conditions exhibit phase
synchronization, which may change for different frequency bands or with
presence of additive system noise. In both cases, Fourier filtering is
traditionally used to preprocess data. We investigate to what extent the phase
synchronization of two coupled R\"{o}ssler oscillators depends on (1) the
broadness of their power spectrum, (2) the width of the band-pass filter, and
(3) the level of added noise. We find that for identical coupling strengths,
oscillators with broader power spectra exhibit weaker synchronization. Further,
we find that within a broad band width range, band-pass filtering reduces the
effect of noise but can lead to a spurious increase in the degree of
synchronization with narrowing band width, even when the coupling between the
two oscillators remains the same.Comment: 4 pages,6 figure
Effect of nonlinear filters on detrended fluctuation analysis
We investigate how various linear and nonlinear transformations affect the
scaling properties of a signal, using the detrended fluctuation analysis (DFA).
Specifically, we study the effect of three types of transforms: linear,
nonlinear polynomial and logarithmic filters. We compare the scaling properties
of signals before and after the transform. We find that linear filters do not
change the correlation properties, while the effect of nonlinear polynomial and
logarithmic filters strongly depends on (a) the strength of correlations in the
original signal, (b) the power of the polynomial filter and (c) the offset in
the logarithmic filter. We further investigate the correlation properties of
three analytic functions: exponential, logarithmic, and power-law. While these
three functions have in general different correlation properties, we find that
there is a broad range of variable values, common for all three functions,
where they exhibit identical scaling behavior. We further note that the scaling
behavior of a class of other functions can be reduced to these three typical
cases. We systematically test the performance of the DFA method in accurately
estimating long-range power-law correlations in the output signals for
different parameter values in the three types of filters, and the three
analytic functions we consider.Comment: 12 pages, 7 figure
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