# 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