WOLFRAM|DEMONSTRATIONS PROJECT

Frequency Distribution of the Logistic Map

​
control parameter a
4
initial value
x
0
0.7
The logistic map is a typical example for dynamical transitions between regular, laminar, and chaotic behavior of a dynamical system. The evolution of the time series depends on the control parameter
a
. The time series is defined by the iterative map
x
n+1
=a
x
n
(1-
x
n
)
.
The frequency distribution shows the frequency of occurrence of different values
x
n
of the resulting time series.
Although the time series changes in the fixed range for different initial values
x
0
, the frequency distribution (outside the fixed points) stays approximately the same.