Chapter 2.4, Problem 1E

Interpretation Introduction

Interpretation:

To classify the fixed points of the given system as stable or unstable using the linear stability analysis. If it is not possible to classify them using linear stability analysis, find the fixed points by graphical analysis.

Concept Introduction:

Using linear stability analysis, the function $\dot{x}$ can be written as $\dot{x}=f\left(x\right)$.

If $f\left(x\right)=0$, then the function is said to be fixed for the given value of $x$.

If for the fixed point $x*$, $f\text{'}\left(x*\right)<0$, then $x*$ is believed to be a stable fixed point.

If for the fixed point $x*$, $f\text{'}\left(x*\right)>0$, then $x*$ is believed to be an unstable fixed point