Chapter 10.3, Problem 4E

Interpretation Introduction

Interpretation:

Consider quadratic map ${\text{x}}_{\text{n+1}}{\text{= x}}_{\text{n}}^{\text{2}}+\text{c}$.

• a) To find and classify all the fixed points as a function of c.

• b) To find the values of c at which the fixed points bifurcate and classify that bifurcation.

• c) To find the values of c for stable $\text{2-}$ cycle and check when it is superstable.

• d) Plot a partial bifurcation diagram for the map and indicate the fixed points, the $\text{2-}$ cycles, and their stability.

Concept Introduction:

• ➢ The difference equation ${\text{x}}_{\text{n+1}}\text{ = f}\left({\text{x}}_{\text{n}}\right)$ the function f is differential function and it is able to solve. The fixed points of the function are those points where the curve of the function meets the green line.