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Time-Series Analysis for Generalized Logistic Maps with z-Unimodality

​
parameter value λ
3.82826
unimodality z
2
initial condition
x
0
0.17738
starting iterate
i
START
0
ending iterate
i
END
=
i
START
+
350
join list
fill bottom
time series opacity
barcode
barcode opacity
This Demonstration shows a time-series plot of an iterative map with a barcode attachment. The test map,
f
GLM
(
x
i
)=
x
i+1
=λ(1-|
x
i
z
|
)2-1
, generalizes the well-known logistic map
f
LM
(
x
i
)=
x
i+1
=λ
x
i
(1-
x
i
)
[1–7]. 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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