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Example: Predator-Prey Model
Example: Predator-Prey Model
Example: Predator-Prey Model
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.
=
Number of rabbits
R
=
Growth rate of rabbits if there are no foxes (use .05)
M
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)
=
Death rate of foxes if there are no rabbits (use .03)
D
Rn
=
R
(1 + M NK W
n-1
=
W
(1 + G R
Wn
n-1
1. On the Y= Editor (8 #), define the sequences and initial values for
u1(n) = u1(nN1) † (1 + .05 N .001 † u2(nN1))
ui1 = 200
u2(n) = u2(nN1) † (1 + .0002 † u1(nN1) N .03)
ui2 = 50
Assume there are initially 200 rabbits and 50 foxes.
Note:
2. Set
Axes = TIME
Sequence Graphing
)
n-1
ND)
n-1
.
and
.
R
W
n
n
370
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