Equilibrium Point

Given

$$y^{\prime }=f(y)$$

An equilibrium point $y_0$ is where $f(y_0)=0$. At such a point, the system’s instantaneous rate of change is at a standstill.

Stability of an Equilibrium Point

$f^{\prime }(y_0)<0⟹$ Asymptotically Stable $f^{\prime }(y_0)>0⟹$ Unstable $f^{\prime }(y_0)=0⟹$ Inconclusive, must analyze deeper using definitions of Stability

Note

$\dim f=1⟺$ $f$ is either asymptotically stable or unstable, but not only stable