A Guided Tour to Wonderland : Visualizing the Slow-Fast Dynamics of an Analytical Dynamical System

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.