Biology Reference
In-Depth Information
1.4
1.2
1
0.8
0.6
0.4
0.2
0
10
20
30
40
50
D
Time
FIGURE 1-19 Cont'd.
x
n
|
x
n
+1
-
x
n
|
| 1 -
x
n
|
1
x
n+
1
0
Time
n
n
+1
FIGURE 1-20.
Source of oscillatory behavior. When ax
n
> 1, the values x
n
and x
nþ1
calculated from Eq. (1-26) will
be on opposite sides of the level 1, causing oscillatory behavior.
We emphasize again that the oscillation behavior here is not possible for
the continuous logistic growth model. For the Verhulst model, the
oscillations are caused by the lag effect described above and not
observed in the logistic model (1-24). As the next section will show,
logistic equations are capable of generating oscillations when explicit
delay is introduced.
Our next exercise presents a discrete population model with long-term
behavior similar to the continuous logistic population model.
