Skip to main content

Symbolic Dynamics from Chaotic Time Series

  • Chapter

Part of the book series: NATO ASI Series ((NSSB,volume 208))

Abstract

Following the ideas of Ruelle and others [1,2], an embedding phase space can be reconstructed from experimental systems on the basis of time series data. The introduction of numerical methods for calculating dimensions, entropies, Lyapunov exponents and other related properties, has permitted extensive investigations of chaotic experimental systems these last years. However, severe restrictions about the applicability of these methods were noticed, especially for high dimensional systems [3–6].

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Eckmann J.P. and Ruelle D., Rev. Mod. Phys. 57 (1985), 617

    Article  MathSciNet  Google Scholar 

  2. Packard N.H., Crutchfield J.P., Farmer J.D. and Shaw R.S.,Phys. Rev. Lett. 45 (1980), 712 F.Takens: in Dynamical systems and turbulence. Eds D.A.Rand & L.S.Young. Lect. Notes in Math. 898, 366 ( Springer, Berlin, 1981 )

    Google Scholar 

  3. Theiler J., Phys. Rev. A 34 (1986) 2427, and references therein.

    Google Scholar 

  4. Babloyantz A. and Destexhe A., in Temporal disorder in human oscillatory systems Eds. L. Rensing, U. an der Heiden and M.C. Mackey, Springer Series in Synergetics 36,48 ( Springer, Berlin, 1987 )

    Google Scholar 

  5. Destexhe A., Sepulchre J.A. and Babloyantz A., Phys. Lett. A 132 (1988), 101.

    Article  Google Scholar 

  6. Eckmann J.P. and Ruelle D., preprint, (1989)

    Google Scholar 

  7. Aizawa Y., Prog. Theor. Phys. 70 (1983), 1249

    MATH  Google Scholar 

  8. Feller W., in: An Introduction to Probability Theory and its Applications ( Wiley, New York, 1957 )

    Google Scholar 

  9. Nicolis G.and Nicolis C., Phys. Rev. A. 38 (1988), 427

    Article  Google Scholar 

  10. Rössler O.E., Ann. N.Y. Acad. Sci. 316 (1979) 376

    Article  Google Scholar 

  11. Nicolis G., Rao G.S., Rao J.S. and Nicolis C., in Structure, Coherence and Chaos in Dynamical Systems, Eds. Christiaensen P.L. and Parmentier R.D. ( Manchester University Press, 1989 )

    Google Scholar 

  12. Kemeny J.G., Snell J.L. and Knapp A.W., in Denumerable Markov Chains, Graduate texts in Mathematics ( Springer, Berlin, 1976 )

    Google Scholar 

  13. A. Destexhe, Phys. Lett. A, in press (1989)

    Google Scholar 

  14. Babloyantz A. and Destexhe A., Biological Cybernetics 58 (1988), 203

    Article  MathSciNet  Google Scholar 

  15. an almost exhaustive state of the art can be found in: Dynamics of Sensory and Cognitive Processing by the Brain Ed. E. Basar, Springer Series in Brain Dynamics vol.1 (1988), vol.2 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Plenum Press, New York

About this chapter

Cite this chapter

Destexhe, A., Nicolis, G., Nicolis, C. (1989). Symbolic Dynamics from Chaotic Time Series. In: Abraham, N.B., Albano, A.M., Passamante, A., Rapp, P.E. (eds) Measures of Complexity and Chaos. NATO ASI Series, vol 208. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0623-9_48

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0623-9_48

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0625-3

  • Online ISBN: 978-1-4757-0623-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics