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DsTool and Dynamical System Toolkits

A dynamical system is defined by a set of rules or transformations for determining how points in a multi-dimensional space move in time. Time may either be discrete or continuous. The traces of the points as they move in discrete or continuous time are called trajectories. The goal of dynamical systems theory is to provide a comprehensive description of the geometric structures arising from these trajectories. In addition to elucidating the dynamics associated to an individual dynamical system, bifurcation theory may be used to describe how the dynamics of a system varies with changes in parameter values.

Interactive numerical and graphical exploration are important tools in dynamical systems research for several reasons:

Consequently, there is a critical need for computational environments that provide effective tools for exploring dynamical systems with minimal effort on the part of the user. Research that relies upon the investigation of dynamical systems would be greatly enhanced by a standard, uniform environment for the exploration of these systems with computers.

The explosion of the graphical computational capabilities of relatively inexpensive desktop computers in the past few years makes the development of such an environment both feasible and timely. This document describes an implementation of one such environment for SunOS, Solaris, SGI, and Linux platforms. The toolkit that we describe is an efficient research tool that integrates a graphical user interface, data management capabilities, and a rich set of numerical algorithms together with the flexibility to add more algorithms and communicate data with other programs. The program, called DsTool (pronounced dee-ess-TOOL), has been implemented for use with the X Window system from MIT. This version uses the Tcl/Tk package by John Ousterhout for its graphical interface. In addition, Geomview is used for three dimensional graphics and animation capabilities. DsTool is based upon the program kaos, written by S. Kim and J. Guckenheimer.


next up previous contents
Next: Attributes of Interface Windows Up: Introduction Previous: Introduction   Contents
2005-10-26