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Cobweb Diagram for Generalized Logistic Maps with z-Unimodality

​
parameter value, λ
4
unimodality, z
2
initial value,
x
0
0.9362
iteration, i
2000
This Demonstration shows the cobweb diagram for
f
GLM
(
x
i
)=
x
i+1
=λ(1-
z
x
i
)2-1
, which generalizes the well-known logistic map
f
LM
(
x
i
)=
x
i+1
=λ
x
i
(1-
x
i
)
[1–8]. Here
i
is the iteration number,
x
i
is the
th
i
iterate of
f
GLM
(
x
i
)
starting from the initial value
x
0
,
λ
is the main control parameter, and
z
is the subcontrol parameter (which determines the unimodality, the degree of the local maximum of
f
GLM
(
x
i
)
).
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