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'
at the cursor point. 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.


c 2001 H. Hohn