Chapter 2.3, Problem 6E

Interpretation Introduction

Interpretation:

To show that the given equation ${\dot{\text{x}}\text{ = s (1 - x) x}}^{\text{a}}{\text{ - (1 - s) x (1 - x)}}^{\text{a}}$ has three fixed points. It is to be shown that for all $\text{a > 1}$, the points at $\text{x = 0}$ and $\text{x = 1}$ are stable fixed point, and the third point ${\text{0 < x}}^{\text{*}}\text{ < 1}$ is an unstable fixed point.

Concept Introduction:

Fixed points are the points where $\dot{\text{x}}\text{ = 0}$. Using this condition, the three fixed points can be found.

The point where the flow is towards it is the stable point, and the point where the flow is away from it is called unstable point.