Fractal Dimension of Strange Attractors from Radius versus Size of Arbitrary Clusters

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3 October 1983

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 51 (14) , 1265-1268
DOI:10.1103/physrevlett.51.1265

Abstract

A fractal dimension

D_{F^{'}}

of strange attractors is estimated as follows. Clusters of

n

nearest-neighbor points are sampled from a time series;

D_{F^{'}}

is found from

{\bar{R}}^{D_{F^{'}}} \sim n

where

\bar{R}

is the average cluster's radius. The estimation of

D_{F^{'}}

is shown to be especially efficient for high dimensional systems.

Keywords

This publication has 8 references indexed in Scilit:

Characterization of Strange Attractors
Physical Review Letters, 1983
Dimension of Strange Attractors
Physical Review Letters, 1980
Statistical Dynamics of Chaotic Flows
Progress of Theoretical Physics, 1980
Scaling theory of percolation clusters
Physics Reports, 1979
The simplest case of a strange attractor
Physics Letters A, 1978
Oscillation and Chaos in Physiological Control Systems
Science, 1977
A two-dimensional mapping with a strange attractor
Communications in Mathematical Physics, 1976
Deterministic Nonperiodic Flow
Journal of the Atmospheric Sciences, 1963