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
Up to New Visualization Ideas for Differential Equations