0. Introduction

Dan Schwalbe (Macalester College) and I have produced a comprehensive Mathematica package for the visualization of differential equations. We call it VisualDSolve; the code and a manual will be published by Springer [SW2]. While most of the functions in it present solutions to DEs in familiar graphical forms, we have introduced several ideas that go beyond what has been commonly done. In this article I will discuss one such feature, the use of shaded nullcline plots to gain insight into the phase plane. Section 1 contains a discussion of an important preliminary function that is very useful in its own right: Equilibria finds all the equilibrium points in a given rectangle. Then section 2 presents the algorithm that produces shaded nullcline plots.

For more information on the overall package, contact me by e-mail. VisualDSolve contains almost 100 functions and a printed manual [SW2] will soon be available. A description of these algorithms also appeared in [SW1].

To use the main functions of this article, Equilibria and NullclinePlot, you will have to load the package by either executing the code in the group above, or placing that group in a file with the right name (NullclinePlot.m on a Macintosh) in the appropriate directory and loading it via Needs["NullclinePlot`"].

Up to New Visualization Ideas for Differential Equations