Using Mutual Information to Estimate Metric Entropy

  • A. M. Fraser
Part of the Springer Series in Synergetics book series (SSSYN, volume 32)

Abstract

A technique for deriving the metric entropy of strange attractors from estimates of the mutual information in scalar time series is presented and applied to experimental and model data. The results are accurate enough to determine if a system is chaotic.

Keywords

Entropy Assure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.N. Kolmogorov, Dokl. Akad. Nauk. SSSR 119, 861 (1958)MATHMathSciNetGoogle Scholar
  2. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 124, 754 (1959)MATHMathSciNetGoogle Scholar
  3. A. N. Kolmogorov, English summary in MR 21, 2035 (1960).Google Scholar
  4. 2.
    Y. Sinai, Dokl. Akad. Nauk. SSSR 124, 768 (1959).MATHMathSciNetGoogle Scholar
  5. A. N. Kolmogorov, English summary in MR 21, 2036 (1960).Google Scholar
  6. 3.
    K. Peterson, Ergodic Theory, (Cambridge University Press, Cambridge, 1983).Google Scholar
  7. 4.
    C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, (University of Illinois Press, Urbana, 1949).MATHGoogle Scholar
  8. 5.
    R. S. Shaw, The Dripping Faucet as a Model Chaotic System, (Aerial Press, Santa Cruz, CA, 1985).Google Scholar
  9. 6.
    N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45., 712 (1980).ADSCrossRefGoogle Scholar
  10. 7.
    F. Takens, in Dynamical Systems and Turbulence, Warwick, 1980, Lecture notes in mathematics Vol. 898, ed. by D. A. Rand and L. S. Young (Springer, Berlin-Heidelberg-New York, 1981), p. 366.Google Scholar
  11. 8.
    W. Krieger, Trans. Amer. Math. Soc. 149, 453 (1970).MATHCrossRefMathSciNetGoogle Scholar
  12. 9.
    J. P. Crutchfield, N.H. Packard, Physica 7D, 153 (1983).MathSciNetGoogle Scholar
  13. 10.
    A. M. Fraser and H. L. Swinney, Phys. Rev. A (1985).Google Scholar
  14. 11.
    A. Brandstater, J. Swift, H. L. Swinney, and A. Wolf, Phys. Rev. Lett. 51, 1442 (1983).ADSCrossRefMathSciNetGoogle Scholar
  15. 12.
    O. E. Rossler, Phys. Lett. 57A, 397 (1976).ADSGoogle Scholar
  16. 13.
    A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, Physica 16D., 285 (1985).ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. M. Fraser
    • 1
  1. 1.Physics Department and the Center for Nonlinear DynamicsThe University of TexasAustinUSA

Personalised recommendations