Chapter 10.3, Problem 3E

Interpretation Introduction

Interpretation:

To analyze the long-term behavior of the map ${\text{x}}_{\text{n+1}}\text{= }\frac{{\text{rx}}_{\text{n}}}{{\text{1+ x}}_{\text{n}}{}^{\text{2}}}$. Also, find and classify all fixed points as a function of r. Find if there be periodic solutions and chaos.

Concept Introduction:

• The fixed points of the function are used to define the stability of the periodic solution.

• The logistic map equation is ${\text{x}}_{\text{n+1}}\text{= }\frac{{\text{rx}}_{\text{n}}}{{\text{1+ x}}_{\text{n}}{}^{\text{2}}}$.