Up: The Geometry Center 1996 Summer Institute

More Discussion of the DS Tool Project

Dynamical systems theory is devoted to studying the equations which model systems that evolve in time. This includes such diverse areas as the motion of pendulums and spacecraft, the flexing of beams and shells, the spread of disease, and the bursting of neurons. In the Geometry Center, we are developing software to aid in the study of such systems of equations. We are interested in students who would like to help us in this effort and in particular to put together demonstration software in hypertext, the language of World Wide Web pages, to show off the capabilities of our computational and visualization software for dynamical systems. This project will be supervised by Patrick Worfolk and Bob Thurman.

DsTool (Dynamical Stystems Toolkit) is a software package for the numerical simulation of dynamical systems. In the Geometry Center we are currently extending its capabilities both in terms of increasing its computational strengths and increasing its visualization abilities. The latter is primarily through interfacing with current Geometry Center software, Geomview, while the former is through implementing and developing algorithms.

This software package is a great way to introduce people to dynamical systems by allowing interactive exploration of many specific equations. However, as with any complicated and flexible software, learning to use it can be difficult. Thus, we are interested in easing this process through a tutorial/demonstration package. It is the development of this package which we view to be the ultimate goal of a summer project.

We envision a document written in hypertext (HTML) which could be distributed with DsTool. This document, viewed through a web browser, would lead users though an interactive demonstration of DsTool. Commands from within the document would start DsTool and take the user through analyses of several dynamical systems. The document would give instructions, discuss the model systems and equations, and initiate a variety of simulations within DsTool. As well as providing a framework from which to learn DsTool, this would also provide a powerful method for implementing a variety of real-time demonstrations of the software.

Students will learn the basics of dynamical systems theory, numerical analysis of dynamical systems, writing hypertext documents, and writing about mathematics. There are also opportunities to study new dynamical systems and implement algorithms not currently in DsTool, but the main focus will be on creating a tutorial/demonstration environment.

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