# Bifurcations of the Logistic Map

Bifurcations of the Logistic Map

The sequence exhibits complicated behavior for certain values of the parameter . When , the sequence converges to a fixed point, but around this fixed point bifurcates into an attracting two-cycle. As increases further, the attractors continue to bifurcate until the sequence displays chaotic behavior around .

x=rx(1-x)

n+1

n

n

r

r<3

r=3

r

r=3.57