Sensitivity to Initial Conditions for the Logistic Map
Sensitivity to Initial Conditions for the Logistic Map
This Demonstration shows the evolution of the distance =- between two orbits of the logistic map =r(1-), where or . The two orbits are initially separated by a perturbation of size . The plot is of || versus for an orbit starting at , perturbation and parameter . An estimate of the error amplification factor and the Lyapunov exponent are shown at the top of the graphic.
E
n
u
n
v
n
x
n+1
x
n
x
n
x=u
v
ϵ=-
u
0
v
0
log
10
E
n
n
x
0
ϵ=
-m
10
r
c
λ=lnc