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The point correlation dimension: Performance with nonstationary surrogate data and noise

  • James E. Skinner
  • Mark Molnar
  • Claude Tomberg
Papers Principles And Algorithms

Abstract

The dynamics of many biological systems have recently been attributed to low-dimensional chaos instead of high-dimensional noise, as previously thought. Because biological data are invariably nonstationary, especially when recorded over a long interval, the conventional measures of low-dimensional chaos (e.g., the correlation dimension algorithms) cannot be applied. A new algorithm, the point correction dimension (PD2i) was developed to deal with this fundamental problem. In this article we describe the details of the algorithm and show that the local mean PD2i will accurately track dimension in nonstationary surrogate data.

Key Words

Chaos theory nonlinear dynamics deterministic models 

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Copyright information

© Springer 1994

Authors and Affiliations

  • James E. Skinner
    • 1
    • 2
  • Mark Molnar
    • 3
  • Claude Tomberg
    • 4
  1. 1.Totts Gap Medical Research LabsBangor
  2. 2.Baylor College of MedicineHouston
  3. 3.Hungarian Academy of SciencesBudapestHungary
  4. 4.University of Brussels Medical SchoolBrusselsBelgium

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