# Controlling Chaos on the Logistic Map

Controlling Chaos on the Logistic Map

Consider the logistic map given by

x=f(x)=μx(1-x)

n+1

μ

n

n

n

μ=4

One method available to control the chaos in this one-dimensional system consists of applying periodic proportional pulses once every iterations ( 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 .

m

x=kx

i

i

i≡0(modm)

m

m=1,2,3,…

k

-1<C(x)<1

m

C(x)=

m

x

f(x)

m

μ

df(x)

m

μ

dx