A Comparison of Correlation and Lyapunov Dimensions
Konstantinos E. Chlouverakis and J. C.
Sprott
Department of Electronic Systems Engineering, University of Essex,
Wivenhoe Park, Colchester CO4 3SQ, UK
Department of Physics, University
of Wisconsin, Madison, WI 53706, USA
Received 14 February 2004; received in revised form 6 September 2004;
accepted 22 October 2004
ABSTRACT
This
paper
investigates the relation between the correlation (D2)
and the Kaplan-Yorke dimension (DKY) of
three-dimensional chaotic flows. Besides the
Kaplan-Yorke dimension, a new Lyapunov dimension (DS),
derived using a polynomial interpolation
instead of a linear one, is compared with DKY
and D2. Various
systems from the literature are used in this analysis together with
some
special cases that span a range of dimension 2 < DKY
< 3. A
linear regression to the
data produces a new
fitted Lyapunov dimension of the form Dfit
= α − βλ1/λ3, where λ1 and λ3 are the largest and smallest
Lyapunov exponents
respectively. This form correlates better with the correlation
dimension D2 than do either DKY
or DS. Additional forms of the fitted
dimension are
investigated to improve the fit to D2, and the results are discussed and interpreted
with
respect to the Kaplan-Yorke conjecture.
Ref: K.
E. Chlouverakis and J. C. Sprott, Physica D 200,
156-164 (2004)
The complete paper is available in PDF
format.
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