Computer Algebra Recipes

2.1. PHASE-PLANE ANALYSIS 77
Next, Eiram will show the time evolution of the two animal populations.
First she uses the textplot commandtocreatenamelabelstobeaddedtothe
¯nal ¯gure.
> tp:=textplot([[1.2,1.1,"sung"],[1.2,2,"gnus"]]):
She then uses the display command and the functional operator F to produce
Figure 2.17, showing the temporal evolution of the gnus and sung populations
for a period of two years. On the computer screen the gnus' population density
is colored red, the sung's population density blue.
> display(fF(t,g,red),F(t,s,blue),tpg,labels=["t",""],
tickmarks=[3,3],view=[0..2,0..3]);
3
2
1
0
gnus
sung
1 t 2
Figure 2.17: Temporal evolution of gnus and sung.
So Eiram concludes that if all conditions remain the same, then the two groups
will ultimately live in relative harmony with each other, since both gnus and
sung survive. However, she notes that the gnus will gain the upper hand in
terms of population density over their more backward relatives, even though
initially the density of sung was twice that of the gnus.
PROBLEMS:
Problem 2-10: Create your own model
Create your own complicated model of the gnus{sung interaction by modifying
the last term in each of the equations. Follow the procedure in the text recipe
and determine the fate of the two populations in your model. Feel free to
experiment with parameter values and initial conditions.