Environmental Engineering Reference
In-Depth Information
IF Yn
1 THEN
Y n þ 1 ¼
<
Y n þ
C 1
ELSE
Y n þ 1 ¼
C 2 *Y n
To learn about the properties of this system we investigate its behaviour for
C 2 ¼
Y n
0.5. The first 1,000 iterations
are discarded to eliminate transient behaviour. We then plot the results with C on the
x -axis and the corresponding simulation results on the y -axis. To survey the model
outcome across a parameter range we start with C 1 ¼
0.5 and start each iteration process with y
¼
0.0 and increase it in small
steps up to 0.7. The result is a highly structured pattern with interesting changes in
periodicities. In the covered range, periods between
þ
2 and infinity approximation
occur (Fig. 1.3 ).
The example shows that simplicity and complexity can be in quite a close
relationship: A radically simplified ecosystem model can exhibit aspects of a fractal
dynamic (see also Chaps. 3 and 11). If we find such a situation where we have
captured complexity in a simple approach, then we have found an interesting
underlying mechanism. This is something that we are looking for in various
Fig. 1.3 Iterating the model
IF Y n
<
1 THEN Y n þ 1
¼
Y n
þ
C 1
ELSE Y n þ 1
¼
Y n -C 2 *Y n ,
C 2
0.5,
C 1 is drawn on the x -axis. Drawn over the according C 1 value, the y -axis shows 500 successive
calculation results which exhibit different periodicities. The first 1,000 iterations of the simulation
for each value of C 1 are not drawn to eliminate transient behaviour
¼
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