Symbolic Dynamics from Chaotic Time Series
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].
KeywordsMarkov Process Lyapunov Exponent Chaotic Dynamic Symbolic Dynamic Chaotic Time Series
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- 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
- Theiler J., Phys. Rev. A 34 (1986) 2427, and references therein.Google Scholar
- 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
- Eckmann J.P. and Ruelle D., preprint, (1989)Google Scholar
- Feller W., in: An Introduction to Probability Theory and its Applications ( Wiley, New York, 1957 )Google Scholar
- 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
- Kemeny J.G., Snell J.L. and Knapp A.W., in Denumerable Markov Chains, Graduate texts in Mathematics ( Springer, Berlin, 1976 )Google Scholar
- A. Destexhe, Phys. Lett. A, in press (1989)Google Scholar
- 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