Extraction of Models from Complex Data

  • H. G. Schuster
Part of the NATO ASI Series book series (NSSB, volume 208)


In this article we are concerned with the problem of prediction and data reduction of complex dynamical systems1. We will try to answer the following questions:
  • How does one have to choose the delaytime τ and the embedding dimension m, in order to obtain an optimal reconstruction of the strange attractor of a chaotic system from the time series of a single variable?

  • How could one use unstable periodic orbits, in order to extract models that can be used for prediction?

  • What is the optimal encoding of the prediction function?


Periodic Orbit Chaotic System Prediction Function Strange Attractor Neighborhood Relation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    For an introduction see e.g. H.G. Schuster, “Deterministic Chaos” second edition, VCH publishers, Weinheim (1988)Google Scholar
  2. 2.
    W. Liebert, K. Pawelzik and H.G. Schuster, to be publishedGoogle Scholar
  3. 3.
    F. Takens, in: Springer Lecture Notes in Mathematics 898, 366 (1981)Google Scholar
  4. 4.
    A.M. Fraser and H.L. Swinney Phys. Rev. 33A, 1134 (1986)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    O.E. Rössler, Phys. Lett 57A, 397 (1976)CrossRefGoogle Scholar
  6. 6.
    K. Pawelzik and H.G. Schuster, to be publishedGoogle Scholar
  7. 7.
    D. Ruelle, “Thermodynamic Formalism” Addison Wesley, Reading (1978)Google Scholar
  8. 8.
    P. Cvitanovic Phys. Rev. Lett 61, 2729 (1988)MathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Auerbach, P. Cvitanovic, J.P. Eckmann, G. Gunartne and I. Procaccia Phys. Rev. Lett 58, 2387 (1987)CrossRefGoogle Scholar
  10. 10.
    J.D. Farmer and J.J. Sidorowich, Phys. Rev. Lett. 59, 845 (1987)MathSciNetCrossRefGoogle Scholar
  11. 11.
    D. Werner, G. Radons and H.G. Schuster, to be publishedGoogle Scholar
  12. 12.
    A.N. Kolmogorov, Dokl Akad. Nauk SSSR 114 (1957); Amer. Soc. Transi. 28 55 (1963)Google Scholar
  13. 13.
    G. Lorentz Approximation of Functions Holt Rinchert and Winston N.Y. (1966)Google Scholar
  14. 14.
    J.P. Kahane, Journ. Approx. Theory 13, 229 (1975)MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • H. G. Schuster
    • 1
  1. 1.Institut für Theoretische Physik und SternwarteUniversität KielDeutschland

Personalised recommendations