Data Requirements for Reliable Estimation of Correlation Dimensions

  • A. M. Albano
  • A. I. Mees
  • G. C. de Guzman
  • P. E. Rapp
Part of the NATO ASI Series book series (NSSA, volume 138)

Abstract

It is not always possible to resolve the dimension of an attractor from a finite data set. The number of data points required depends on the structure of the attractor, the distribution of points on the attractor, and the precision of the data. If the chaotic component of a system’s behaviour is sufficiently small relative to its large scale motion, and if orbits seldom visit the region of the attractor with small scale fractal structure, any method will fail to resolve the attractor’s dimension. It is simple to construct abstract mathematical examples that present this behaviour. However, while these limitations should be explicity recognised, it should also be noted that a growing body of empirical experience suggests that experimentally encountered physical and biological systems do not invariably display these behaviours. It is possible to estimate reliably the dimension of these attractors with comparatively small data sets.

Keywords

Entropy Mercury Autocorrelation Lution Xenon 

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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • A. M. Albano
    • 1
  • A. I. Mees
    • 2
  • G. C. de Guzman
    • 3
  • P. E. Rapp
    • 4
  1. 1.Department of PhysicsBryn Mawr CollegeBryn MawrUSA
  2. 2.Department of MathematicsUniversity of Western AustraliaNedlandsUSA
  3. 3.Center for Complex SystemsFlorida Atlantic UniversityBoca RatonUSA
  4. 4.Department of Physiology and BiochemistryMedical College of PennsylvaniaPhiladelphiaUSA

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