Texas Instruments TI-89 Titanium

Sequence Graphing 357
Example: Predator-Prey Model
Using the predator-prey model in biology, determine the numbers of rabbits and foxes
that maintain population equilibrium in a certain region.
1. On the Y= Editor (8#), define the sequences and initial values for
R
n
and W
n
.
u1(n) = u1(nN1) † (1 + .05 N .001 † u2(nN1))
ui1 = 200
u2(n) = u2(nN1) † (1 + .0002 † u1(nN1) N .03)
ui2 = 50
Note: Assume there are initially 200 rabbits and 50 foxes.
2. Set
Axes = TIME.
R
= Number of rabbits
M
= Growth rate of rabbits if there are no foxes (use .05)
K
= Rate at which foxes can kill rabbits (use .001)
W
= Number of foxes
G
= Growth rate of foxes if there are rabbits (use .0002)
D
= Death rate of foxes if there are no rabbits (use .03)
Rn
=R
n-1
(1 + M NK W
n-1
)
Wn
=W
n-1
(1 + G R
n-1
ND)