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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 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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