The method introduced in these examples for Mathematica can NOT be
used for nonlinear system phase-plane plot.  There is another very
nice package which plot the trajectories for nonlinear systems. It
is written in matlab.

To start the package, type "matlab" on a sun workstation. Inside matlab,
type "pplane5" (phase-plane software version 5). In the pop-up windows,
type in the equations, change the maximum and minimun values to include
all critical points, then click "proceed".  In the phase plane pop-up
windows, you may click on any point to get a trajectory through that
point. click several points to get a typical representation of
the phase-plane.