Classifying the Visualization of Analytically

In this paper we suggest a classiication of visualization techniques for analytically speciied dynamical systems into four diierent approaches. We distinguish between local properties, the topology of behavior, global properties, and classes of dynamical systems with respect to various topics of visualization. By presenting advanced visualization techniques that we applied during three recent projects, we discuss their embedding within the classiication scheme. The dynamical systems visualized are the \Dynastic Cycle", which is a model for rise and fall of dynasties in ancient China, the \Wonderland" model, that simulates the interactions of population growth, economic activities, and environmental pollution, and a model for mixed-mode oscillations, which occurs in chemistry.