Feigenbaum's Scaling Relation for Superstable Parameter Values: "Bifurcation Diagram Helper"
Feigenbaum's Scaling Relation for Superstable Parameter Values: "Bifurcation Diagram Helper"
As the fixed points of the iterated function =f()=λ(1-) approach chaotic behavior with repeated period doubling, the superstable parameter value approaches its limiting value , known as the Feigenbaum point. As the value of (the order of the period-doubling bifurcation) increases, Feigenbaum's scaling relation between the three adjacent superstable parameter values approaches a universal limit known as Feigenbaum's constant [1–7], that is,
x
i+1
x
i
x
i
x
i
λ
r
λ
∞
r
δ=4.6692016…
lim
r∞
λ
r
λ
r+1
λ
r+1
λ
r+2