A measure
of a strange attractor which allows the presence
of chaos to be distinguished from random noise. It is related
to the capacity dimension
and information dimension
, satisfying
![nu<=sigma<=D.](/images/equations/CorrelationExponent/NumberedEquation1.svg) |
(1)
|
It satisfies
![nu<=D_(KY),](/images/equations/CorrelationExponent/NumberedEquation2.svg) |
(2)
|
where
is the Kaplan-Yorke dimension. As the cell
size goes to zero,
![lim_(epsilon->0)nu->D_2,](/images/equations/CorrelationExponent/NumberedEquation3.svg) |
(3)
|
where
is the correlation dimension.
See also
Correlation Dimension,
Information Dimension,
Kaplan-Yorke
Dimension
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References
Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983.Referenced
on Wolfram|Alpha
Correlation Exponent
Cite this as:
Weisstein, Eric W. "Correlation Exponent."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CorrelationExponent.html
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