Chapter 2.4, Problem 4E

Interpretation Introduction

Interpretation:

Fixed points of the system ${\dot{\text{x}}\text{ = x}}^{\text{2}}\text{(6 - x)}$ are to be classified using linear stability analysis, and if it fails, by using graphical argument.

Concept Introduction:

Fixed points of a system are the points where $\dot{\text{x}}\text{ = 0}$, and are denoted by ${\text{x}}^{\ast }$

When ${\text{f '(x}}^{\ast })<0$, the fixed point is stable.

When ${\text{f '(x}}^{\ast })>0$, the fixed point is unstable.

The stability of the fixed point can’t be determined by linear analysisif ${\text{f '(x}}^{\ast })=0,$ and graphical argument should be used.

Semi stable points are the points at which the local flow is towards them as well as away from them.