Phase
Lines -- Help |
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. A yellow vector parallel with the slope field
is displayed at the cursor point. Clicking creates the solution curve
through that point. There is a readout of the values of t, y, and y' 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 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.
c
2001 H. Hohn |