Complexity Explorer Santa Few Institute

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Introduction to Dynamical Systems and Chaos (2021)

Lead instructor: Patricia Mellodge

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6.2 Universality in Maps » Quiz 2

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Instructions: Recall the following definitions from the previous video:

$\Delta_1 = r_2 -r_1$

and,

$\delta_1 = \frac{\Delta_1}{\Delta_2}=\frac{r_2-r_1}{r_3-r_2}$

And in general,

$\Delta_n = r_n_+_1-r_n$

and,

$\delta_n =\frac{\Delta_n}{\Delta_n_+_1}=\frac{r_n_+_1 -r_n}{r_n_+_2-r_n_+_1}$ .

From the cubic equation, the bifurcation occur at the following values:

$r_1=5.333333$

$r_2=5.763643$

$r_3=5.8610233$

$r_4=5.882110$