LINEAR PHASE PORTRAITS: CURSOR ENTRY

The graphing window at right displays a few trajectories of the linear system \(\dot{x} = Ax\). Below the window the name of the phase portrait is displayed, along with the matrix \(A\) and the eigenvalues of \(A\).

To control the matrix one first sets the trace and the determinant by dragging the cursor over the diagram at bottom left or by grabbing the sliders below or to the left of that diagram. Select from among the matrices with given trace and determinant by dragging the cursor over the window at upper left, or by grabbing the sliders below and to the left of that window. The bottom slider conjugates the matrix \(A\) by a rotation matrix; the effect is to rotate the phase portrait. The left slider controls the "asymmetry" of \(A\), half the difference of between its off-diagonal entries. When the eigenvalues are not real, the asymmetry is at least the imaginary part of the eigenvalue in absolute value, so the upper left window splits into two portions (corresponding to clockwise or counterclockwise spirals).

Depress the mousekey over the graphing window to display a trajectory through that point. The trajectory can be dragged by moving the cursor with the mousekey depressed. Releasing it will leave the trajectory in place. Click on [Clear] to clear all the trajectories.

© 2001 H. Hohn and H. Miller