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

Integrative Physiological and Behavioral Science volume 29, pages 217–234 (1994)Cite this article

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.

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Author information

Affiliations

  1. Director of Research, Totts Gap Medical Research Labs, RR#1 Box 1120G, 18013, Bangor, PA

    James E. Skinner

  2. Director of Research, Baylor College of Medicine, Houston, Texas

    James E. Skinner

  3. Hungarian Academy of Sciences, Budapest, Hungary

    Mark Molnar

  4. University of Brussels Medical School, Brussels, Belgium

    Claude Tomberg

Authors
  1. James E. Skinner
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  2. Mark Molnar
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  3. Claude Tomberg
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Additional information

Research support by NIH, NS 27745.

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Skinner, J.E., Molnar, M. & Tomberg, C. The point correlation dimension: Performance with nonstationary surrogate data and noise. Integrative Physiological and Behavioral Science 29, 217–234 (1994). https://doi.org/10.1007/BF02691327

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  • DOI: https://doi.org/10.1007/BF02691327

Key Words

  • Chaos theory
  • nonlinear dynamics
  • deterministic models