Sensitivity to Initial Conditions for the Logistic Map

u

0

0.202

m

16

(ϵ =

-m

10

)

r

4

This Demonstration shows the evolution of the distance

E

n

=

u

n

-

v

n

between two orbits of the logistic map

x

n+1

=r

x

n

(1-

x

n

)

, where

x=u

or

v

. The two orbits are initially separated by a perturbation of size

ϵ=

u

0

-

v

0

. The plot is of

log

10

|

E

n

|

versus

n

for an orbit starting at

x

0

, perturbation

ϵ=

-m

10

and parameter

r

. An estimate of the error amplification factor

c

and the Lyapunov exponent

λ=lnc

are shown at the top of the graphic.