Chapter 10.3, Problem 2E

Interpretation Introduction

Interpretation:

Let $\text{p}$ and $\text{q}$ be points in a $\text{2-}$ cycle for the logistic map.

• a) To show that if the cycle is superstable, then either $\text{p =}\frac{1}{2}$ or $\text{q =}\frac{1}{2}$.

• b) To find out the value of r at which the logistic map has a super stable 2-cycle.

Concept Introduction:

• ➢ Super stable points are the fixed points (${\text{x}}^{*}$) of an interval map $\text{T}$, when ${\text{T(x}}^{*})=0$.

• ➢ The logistic map equation is $\text{f}\left(\text{x}\right)\text{ = rx}\left(\text{1-x}\right)$.

• ➢ The logistic equation is a different equation which is defined as the fixed point of the map in the interval $\left[0,4\right]$ and also which determines the stability of the logistic map.