Chapter 10.4, Problem 2E

Interpretation Introduction

Interpretation:

To analyze the map ${\text{x}}_{\text{n+1}}\text{=}\frac{\text{r}{\left({\text{x}}_{\text{n}}\right)}^{\text{2}}}{\text{1+}{\left({\text{x}}_{\text{n}}\right)}^{\text{2}}}$. Find and classify all the bifurcation and draw the bifurcation diagram. Can this system exhibit intermittency?

Concept Introduction:

• Determine the fixed points for the given equation and its stability.

• Obtain the bifurcation equation from the given map.

• Plot the bifurcation diagram for different values of $\text{r}$.