Journal of Nonlinear Science

, Volume 1, Issue 2, pp 147–173

Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction

  • G. B. Mindlin
  • H. G. Solari
  • M. A. Natiello
  • R. Gilmore
  • X. -J. Hou
Article

DOI: 10.1007/BF01209064

Cite this article as:
Mindlin, G.B., Solari, H.G., Natiello, M.A. et al. J Nonlinear Sci (1991) 1: 147. doi:10.1007/BF01209064

Summary

We have applied topological methods to analyze chaotic time series data from the Belousov-Zhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a three-dimensional embedding without self-intersections was constructed from the data set. The topological structure of that flow was visualized by constructing a branched manifold such that every periodic orbit in the flow could be held by the branched manifold. The branched manifold, or induced template, was computed using the three lowest-period orbits. The organization of the higher-period orbits predicted by this induced template was compared with the organization of the orbits reconstructed from the data set with excellent results. The consequences of the presence of certain knots found in the data are discussed.

Key words

strange attractor template time series data 

Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • G. B. Mindlin
    • 1
  • H. G. Solari
    • 1
  • M. A. Natiello
    • 3
  • R. Gilmore
    • 1
  • X. -J. Hou
    • 1
  1. 1.Department of Physics and Atmospheric ScienceDrexel UniversityPhiladelphiaUSA
  2. 2.Departamento de FísicaFCEN-Universidad de Buenos Aires, Pabellón I, Ciudad UniversitariaBuenos AiresArgentina
  3. 3.Department of Quantum ChemistryUppsala University20 UppsalaSweden

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