WOLFRAM|DEMONSTRATIONS PROJECT

Power Spectrum of the Logistic Map

​
control parameter a
4
initial value
x
0
0.7
The power spectrum shows the energy distribution over different frequencies of a time series.
The logistic map is a prototypical example for dynamical transitions between regular, laminar, and chaotic behaviors of a dynamical system. The evolution of the time series depends on the control parameter
a
and the initial value
x
0
. The time series is defined by the iterative map
x
n+1
=a
x
n
(1-
x
n
)
.
Although the time series changes for different initial values
x
0
with fixed control parameter
a
, the power spectrum (outside the fixed points) stays approximately the same.