Computer Algebra Recipes

1.1. PHASE-PLANE PORTRAITS 21
J
1
0.5
–1 –0.5 0 0.5
R
1
–0.5
–1
Figure 1.4: Phase-plane portrait for the love a®air.
By introducing the option scene=[t,R] into phaseportrait, a plot of R
vs. t can be produced. The resulting picture for the ¯rst initial condition is
shown in Figure 1.5, Romeo's initial hate turning to love. Changing R to J in
the scene option will generate J versus t. Try it and see how Juliet responds.
> phaseportrait([de1,de2],[R(t),J(t)],t=0..2,[[ic1]],
stepsize=0.2,scene=[t,R],color=red,linecolor=blue);
R
0.6
0.4
0.2
0
–0.2
0.5 1 1.5 2
t
Figure 1.5: R versus t for the love a®air.