Chapter 6: Sequence Graphing
111
6. Press
p
and change the variables below.
7. Press
s
to graph the sequence.
8. Press
r
, and then press
~
to draw the web. The displayed cursor coordinates
n
,
X
(
u(
n
N
1)
),
and
Y
(
u(
n
)
) change accordingly. When you press
~
, a new
n
value is displayed, and the trace
cursor is on the sequence. When you press
~
again, the
n
value remains the same, and the
cursor moves to the
y=x
reference line. This pattern repeats as you trace the web.
Graphing Phase Plots
Graphing with uv, vw, and uw
The phase-plot axes settings
uv
,
vw
, and
uw
show relationships between two sequences. To
select a phase-plot axes setting, press
y
.
, press
~
until the cursor is on
uv
,
vw
, or
uw
,
and then press
Í
.
Example: Predator-Prey Model
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 foxes and rabbits, with
initial populations of 200 rabbits (
u(
n
Min)
) and 50 foxes (
v(
n
Min)
).
These are the variables (given values are in parentheses):
Xmin=
L
10
Xmax=10
Axes Setting
x-axis
y-axis
uv
u(
n
)
v(
n
)
vw
v(
n
)
w(
n
)
uw
u(
n
)
w(
n
)
R
= number of rabbits
M
= rabbit population growth rate without foxes
(.05)
K
= rabbit population death rate with foxes
(.001)
W
= number of foxes
G
= fox population growth rate with rabbits
(.0002)
