Chapter 10.2, Problem 1E

Interpretation Introduction

Interpretation:

For all real $\text{x}$ to show that if ${\text{x}}_{\text{n}}\text{>1}$ for some n, then subsequent iterations diverge toward $\text{-}\infty$. Also, explain why it is sensible to restrict $\text{r}$ and $\text{x}$ to the intervals $\text{r}\in \left[\text{0,4}\right]$ and $\text{x}\in \left[\text{0,1}\right]$.

Concept Introduction:

• ➢ Logistic Map: A logistic map is defined as the polynomial map of the degree two and chaotic behavior can arise from a non-linear dynamic equation.

• ➢ Flip bifurcation is often associated with period-doubling.