Visualizing 3D Dynamical Systems on the Basis of Poincare Maps
Talk in Prague, May 21, 1997.
Dynamical systems are often used to describe a set of variables
which change over time. Real world phenomena as, e.g., food
chains, can be modeled by the concept of a dynamical system. A
Poincare map is a mathematical abstraction, which if often used to
examine a periodic or quasi-periodic dynamical systems. A set of
advanced visualization techniques is presented, which are based on
the idea of integrating the visualization of the 2D Poincare map
with a representation of the underlying 3D flow. For example,
drawing the trajectory which constructs the Poincare map can be
useful to provide additional insights. Images that were rendered
using our implementation of these techniques are shown to
demonstrate the possibilities of this approach.
Last update: June 25, 1997.
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Vienna University of Technology.