Chapter 10.3, Problem 5E

Interpretation Introduction

Interpretation:

To show that the logistic map ${\text{x}}_{\text{n+1}}{\text{= rx}}_{\text{n}}{\text{(1- x}}_{\text{n}}\text{)}$ can be transformed into a quadratic map ${\text{y}}_{\text{n+1}}{\text{= y}}_{\text{n}}^{\text{2}}+\text{c}$ by the linear change of variables, ${\text{x}}_{\text{n}}{\text{= ay}}_{\text{n}}\text{+ b}$ where $\text{a}$ and $\text{b}$ to be determined.

Concept Introduction:

• ➢ Conjugacy is a change of variable that converts one map into another map.

• ➢ By converting one map into another map and comparing it with the given map we can find the values of $\text{a}$ and $\text{b}$.