Correlation Exponent
A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information dimension sigma, satisfying
| nu<=sigma<=D. |
(1)
|
It satisfies
| nu<=D_(KY), |
(2)
|
where D_(KY) is the Kaplan-Yorke dimension. As the cell size goes to zero,
| lim_(epsilon->0)nu->D_2, |
(3)
|
where D_2 is the correlation dimension.
See also
Correlation Dimension, Information Dimension, Kaplan-Yorke DimensionExplore with Wolfram|Alpha
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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 ExponentCite this as:
Weisstein, Eric W. "Correlation Exponent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CorrelationExponent.html