Bifurcation Diagram for a Generalized Logistic Map
Bifurcation Diagram for a Generalized Logistic Map
This Demonstration shows a bifurcation diagram for a generalized logistic map, [1–7]. This map is very wellsuited for numerical analysis because:
f()==(1)1
x
n
x
n+1
λ
2
x
n
z

1. The basin of attraction for an attracting set is strictly confined within for any initial value and for any parameter values and .
x≤1
x
0
λ>0
z>0
2. The basin of attraction for an attracting set abruptly vanishes at for any value of , that is, "all boundary crises occur at ."
λ=4
z
λ=4
3. Since the function is symmetric around , this map is particularly convenient for renormalization group analysis.
f(x)
x=0
The blue box on the left is the locator where the image inside the box is rescaled on the right in accordance with the zoomin level . By dragging the locator, you can change where to zoom in.
ζ