Texas Instruments TI-86 - Predator-Prey Model

258
Chapter 19: Applications
19APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 258 of 1819APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 258 of 18
Predator-Prey Model
The growth rates of predator and prey populations, such as foxes and rabbits, depend upon the
populations of both species. This initial-value problem is a form of the predator-prey model.
F'=
L
F+0.1F
¹
R R'=3R
N
F
¹
R
Q1
= population of foxes (F)
Q2
= population of rabbits (R)
Q
[
1
= initial population of foxes (2)
Q
[
2
= initial population of rabbits (5)
Find the population of foxes and rabbits after 3 months (
t=3
).

In
DifEq
graphing mode, select
Q't=
from the
GRAPH
menu and enter the functions and set graph
styles in the equation editor as shown.
¼Q'1=
L
Q1+0.1Q1¹Q2 »Q'2=3Q2
N
Q1¹Q2

Select
FORMT
from the
GRAPH
menu and set
FldOff
field format.

Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
tMin=0 xMin=
L
1 yMin=
L
10
tMax=10 xMax=10 yMax=40
tStep=
pà
24 xScl=5 yScl=5
tPlot=0 difTol=.001

Select
INITC
from the
GRAPH
menu and set the initial conditions as shown.
tMin=0 Q
[
1=2 Q
[
2=5