Chapter 10.1, Problem 11E

Interpretation Introduction

Interpretation:

For the map ${\text{x}}_{n+1}{\text{ = 3x}}_n-{\text{x}}^3{}_{\text{n}}$, find all the fixed points and determine their stability. Draw the cobweb starting at ${\text{x}}_0=1.9$ and ${\text{x}}_0=2.1$. Explain the dramatic difference between the cobweb of ${\text{x}}_0=1.9$ and ${\text{x}}_0=2.1$, also prove that the orbit will remain bounded for all $\text{n}$ or $\left|{\text{x}}_n\right|\to \infty$.

Concept Introduction:

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

• ➢ Plot the cobweb for the given initial value.