Chapter 2.4, Problem 2E

Interpretation Introduction

Interpretation:

By using linear stability analysis, fixed points of the $\dot{\text{x}}\text{=x}\left(\text{1-x}\right)\left(\text{2-x}\right)$ are to be determined. If the linear stability analysis fails, then use a graphical argument to decide the stability.

Concept Introduction:

First, find the fixed point for the equation $\dot{\text{x}}\text{=x}\left(\text{1-x}\right)\left(\text{2-x}\right)$. The condition for the fixed point is $\dot{\text{x}}\text{=0}$.

Stable points are points at which the local flow is toward them. They represent stable equilibria at which small disturbances damps out in time away from it.

Unstable points are points at which the local flow is away from them. They represent unstable equilibria.