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Fig. 5.13
The curves of some simple growths
therefore, the final formula is obtained:
k
n
+
1
−
1
G
(
n
)=
1
.
k
−
Figure 5.13 shows many kinds of growth functions.
Sigmoid functions occur when growth processes are between two thresholds and
the growth rate is inversely proportional to the growth level. This happens, for ex-
ample, in the exponential sigmoid 2
e
−
t
displayed in Fig. 5.14.
Hill functions are another kind of
sigmoid functions
with shapes such as that
one displayed in Fig. 5.15:
/
(
1
+
)
Ax
n
B
n
H
(
x
)=
x
n
.
+
5.6.4
Logistic Maps
The
logistic map
is a a growth rule which provides the fraction of living individuals,
in a population having a maximum size denoted by 1. If
x
denotes the fraction of liv-
ing individuals, then
f
(
)
represents the fraction of them at the next generation (like
in the previous cases, the process evolves along a discrete sequence of generation
steps):
x
