Chapter 12.6, Problem 9E

In Problems 5 -12 , either by hand or using computer software package, sketch the phase plane diagram for the given system. Discuss the stability of each limit cycle and critical point. Here $x=r\cos \theta$ and $y=r\sin \theta$.

$\frac{dx}{dt}=x+y+x\left(r^2-3r+r\right)$

$\frac{dy}{dt}=-x+y+y\left(r^2-3r+r\right)$