Graphing Phase Plots - Texas Instruments TI-83 Manual Book

Graphing Phase Plots

Graphing with uv,
vw, and uw
Example:
Predator-Prey
Model
The phase-plot axes settings
relationships between two sequences. To select a
phase-plot axes setting, press y [
the cursor is on
uv
Axes Setting
uv
vw
uw
Use the predator-prey model to determine the regional
populations of a predator and its prey that would maintain
population equilibrium for the two species.
This example uses the model to determine the equilibrium
populations of wolves and rabbits, with initial populations
of 200 rabbits (
u( n Min)
These are the variables (given values are in parentheses):
R = number of rabbits
M = rabbit population growth rate without wolves
K = rabbit population death rate with wolves
W = number of wolves
G = wolf population growth rate with rabbits
D = wolf population death rate without rabbits
= time (in months)
n
R = R (1+MNKW
n n N1
W = W (1+GR
n n N1
1. Press o in
Seq
Define the sequences and initial values for R
shown below. Enter the sequence R
the sequence W
, , and
uv vw
FORMAT
, and then press Í.
, , or
vw uw
x-axis
u( n )
v( n )
u( n )
) and 50 wolves (
)
n N1
ND)
n N1
mode to display the sequence
as .
v( n )
n
Sequence Graphing 6-13
show
uw
], press ~ until
y-axis
v( n )
w( n )
w( n )
).
v( n Min)
(.05)
(.001)
(.0002)
(.03)
editor.
Y=
and W
n n
as and enter
u( n )
n
as