INTERACTIVE GRAPHICAL EXPLORATION OF MULTIDIMENSIONAL NONLINEAR DYNAMICAL SYSTEMS

Abstract

This paper discusses the application of an inherently three-dimensional graphical representation tool, isosurfaces, as a means to interactively explore and visualize the attractors of a nonlinear dynamical system with a fifteen-dimensional parameter space. A program has been written which allows the scientist to interactively select and visualize three-dimensional sub-spaces of the fifteen-dimensional parameter space. The dynamical system used to illustrate these concepts is a discrete-time, nonlinear, three-nation Richardson model with economic constraints. This dynamical system, which models the shifting alliances of nations in an arms race, maps an initial point in the unit cube to another point in the unit cube after multiple iterations of the model functions. Using an isosurface function on the resulting volumetric data set, surfaces indicating the changing alliances of nations are generated and rendered.