Graphics Programs Reference
In-Depth Information
suggests the possibility of unstable periodic cycles and other recurring
phenomena. Indeed a great deal of information is known. The
aforementioned book by Gulick is a fine reference, as well as the source of an
excellent bibliography on the subject.
Rerunning the Model with SIMULINK
The logistic growth model that we have been exploring lends itself
particularly well to simulation using SIMULINK. Here is a simple
SIMULINK model that corresponds to the above calculations:
1
1
−
x
z
Product
Unit Delay
u
x
1
1
Logistic
Constant
3.7
Scope
x
Discrete Pulse
Generator
Let's briefly explain how this works. If you ignore the Discrete Pulse
Generator block and the Sum block in the lower left for a moment, this
model implements the equation
x
at next time
=
ux
(1
−
x
) at old time
,
which is the equation for the logistic model. The Scope block displays a plot
of
x
as a function of (discrete) time. However, we need somehow to build in
the initial condition for
x
. The simplest way to do this is as illustrated here:
We add to the right-hand side a discrete pulse that is the initial value of
x
at
time
t
=
0 and is 0 thereafter. Since the model is discrete, you can achieve
this by setting the period of the Discrete Pulse Generator block to something
longer than the length of the simulation, and setting the width of the pulse
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