, Volume 1, Issue 2, pp 147173
First online:
Topological analysis of chaotic time series data from the BelousovZhabotinskii reaction
 G. B. MindlinAffiliated withDepartment of Physics and Atmospheric Science, Drexel University
 , H. G. SolariAffiliated withDepartment of Physics and Atmospheric Science, Drexel University
 , M. A. NatielloAffiliated withDepartment of Quantum Chemistry, Uppsala University
 , R. GilmoreAffiliated withDepartment of Physics and Atmospheric Science, Drexel University
 , X. J. HouAffiliated withDepartment of Physics and Atmospheric Science, Drexel University
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We have applied topological methods to analyze chaotic time series data from the BelousovZhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a threedimensional embedding without selfintersections 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 lowestperiod orbits. The organization of the higherperiod 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 Title
 Topological analysis of chaotic time series data from the BelousovZhabotinskii reaction
 Journal

Journal of Nonlinear Science
Volume 1, Issue 2 , pp 147173
 Cover Date
 199106
 DOI
 10.1007/BF01209064
 Print ISSN
 09388974
 Online ISSN
 14321467
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 strange attractor
 template
 time series data
 Authors

 G. B. Mindlin ^{(1)}
 H. G. Solari ^{(1)}
 M. A. Natiello ^{(3)}
 R. Gilmore ^{(1)}
 X. J. Hou ^{(1)}
 Author Affiliations

 1. Department of Physics and Atmospheric Science, Drexel University, 19104, Philadelphia, PA, USA
 3. Department of Quantum Chemistry, Uppsala University, Box 518, S751, 20 Uppsala, Sweden