Controlling Chaos on the Logistic Map
Controlling Chaos on the Logistic Map
Consider the logistic map given by
x
n+1
f
μ
x
n
x
n
x
n
μ=4
One method available to control the chaos in this one-dimensional system consists of applying periodic proportional pulses once every iterations (=k when ). The number of fixed points is equal to . For a specific choice of , there are only a few values of that stabilize the logistic map. These ranges are restricted to , where (x)=(x).
m
x
i
x
i
i≡0(modm)
m
m=1,2,3,…
k
-1<(x)<1
m
C
m
C
x
m
f
μ
d(x)
m
f
μ
dx