Complexity Explorer Santa Fe Institute

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Introduction to Dynamical Systems and Chaos (Fall 2018)

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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