Sequence Graphing 371
Example: Predator-Prey Model
Example: Predator-Prey ModelExample: 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.
1. On the Y= Editor (8#), define the sequences and initial values for Rn and Wn.
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 50foxes.
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 Wn-1)
Wn =W
n-1 (1 + G R n-1 ND)