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Abstract

The analysis of complex dynamical systems produces large amounts of data that have to be interpreted efficiently. Visualizing the phase space of such systems illustrates geometrically the behavior of the underlying dynamics. This work investigates the visualization of Wonderland, a four dimensional econometric model, which describes interactions between population growth, economic activity and environmental implications. Wonderland belongs to a class of interesting dynamical systems with a pronounced slow-fast dynamics, i.e., some variables are changing much faster than others. Furthermore the behavior of the Wonderland model is characterized by manifolds which are not streamsurfaces, i.e., the flow does not stay within these surfaces. This paper discusses the application and adaptation of various visualization techniques to analytical dynamical systems with special properties as mentioned above.

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@techreport{wegenkittl-1996-GTW,
  title =      "A Guided Tour to Wonderland: Visualizing the Slow-Fast
                Dynamics of an Analytical Dynamical System",
  author =     "Rainer Wegenkittl and Meister Eduard Gr{\"o}ller and Werner
               Purgathofer",
  year =       "1996",
  abstract =   "The analysis of complex dynamical systems produces large
               amounts of data that have to be interpreted efficiently.
               Visualizing the phase space of such systems illustrates
               geometrically the behavior of the underlying dynamics. This
               work investigates the visualization of Wonderland, a four
               dimensional econometric model, which describes interactions
               between population growth, economic activity and
               environmental implications. Wonderland belongs to a class of
               interesting dynamical systems with a pronounced slow-fast
               dynamics, i.e., some variables are changing much faster than
               others. Furthermore the behavior of the Wonderland model is
               characterized by manifolds which are not streamsurfaces,
               i.e., the flow does not stay within these surfaces. This
               paper discusses the application and adaptation of various
               visualization techniques to analytical dynamical systems
               with special properties as                 mentioned above.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      apr,
  number =     "TR-186-2-96-11",
  keywords =   "vector field visualization, complex dynamical systems",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1996/wegenkittl-1996-GTW/",
}