Chapter 10.4, Problem 1E

Interpretation Introduction

Interpretation:

To analyze the map ${\text{x}}_{\text{n+1}}\text{= rexp}\left({\text{x}}_{\text{n}}\right)$ usinga cobweb. Show that a tangent bifurcation occurs at $\text{r = 1/e}$. Sketch the time series ${\text{x}}_{\text{n}}$ vs $\text{n}$ for $\text{r}$ just above and just below $\text{r = 1/e}$.

Concept Introduction:

• Plot the cobweb for the given function with different $\text{r}$ values.

• Observe the graph to obtain bifurcation.

• Plot the time series plot of ${\text{x}}_{\text{n}}$.