Select
an autonomous ODE using the popdown menu [v] at bottom center.
The
main graphing window displays the direction field and any equilibrium
solutions. Stable equilibria are indicated in green, unstable in red,
and semistable in cyan. When the cursor is placed over the graphing window a yellow vector parallel
with the vector field is displayed, and the values of t, y, and y' are read out. When the mousekey
is depressed, the solution though that point is displayed. When the mousekey is released, the solution remains. Solution curves can be cleared by pressing the
[Clear] key.
The
graphing window at lower left displays y' as a function of y.
Each
of the menu choices includes a parameter a which can be set using a
slider at lower right.
Selecting
the Phase Line checkbox displays the phase line. On it are drawn critical
points (in green, red, or cyan) and a few direction arrows. As solutions
are drawn on the graphing window, the corresponding trajectory is traced
out on the phase line. Clicking on the phase line at a value y causes
the solution through (0, y) to be drawn on the graphing window. Clicking the [Clear] key under the phase line
clears the trajectories.
Selecting
the Bifurcation Diagram checkbox reveals the bifurcation diagram, which
displays the locus of critical points, colored green, red, or cyan.
The phase line for the selected value of a is also displayed.
©
2001 H. Hohn