Chapter 10.4, Problem 4E

Interpretation Introduction

Interpretation:

Approximate the value of $\text{r}$ at which the logistic map ${\text{x}}_{\text{n+1}}\text{= 1 - r}{\left({\text{x}}_{\text{n}}\right)}^2$ has a superstable $3$-cycle. Give a numerical approximation that is accurate to at least four places after the decimal point.

Concept Introduction:

• Determine the fixed points for the given equation.

• Compute ${\text{f}}^{\text{3}}\left(\text{x}\right)\text{ = x}$, and plug the fixed point.

• Obtain the value of $\text{r}$ from the cycle -$3$.