“Correlation Dimension”的概念、定义、习题解题方法及翻译-数学辞典

单词

Correlation Dimension

释义

Correlation Dimension

Define the correlation integral as

(1)

where

is the Heaviside Step Function. When the below limit exists, the correlation dimension is thendefined as

(2)

is the Correlation Exponent, then

(3)

It satisfies

(4)

To estimate the correlation dimension of an -dimensional system with accuracy requires data points, where

(5)

where

is the length of the ``plateau region.'' If an Attractorexists, then an estimate of

saturates above some

given by

(6)

which is sometimes known as the fractal Whitney embedding prevalence theorem.

See also Correlation Exponent, q-Dimension

References

Nayfeh, A. H. and Balachandran, B. Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. New York: Wiley, pp. 547-548, 1995.

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