Chapter 12.RP, Problem 14RP

In Problem 13 and 14, sketch the phase plane diagrams for the given system. Discuss the stability of each limit cycle and critical point.

Here $x=r\cos \theta$ and $y=r\sin \theta$.

$\begin{array}{rll}\frac{dx}{dt}& =& x-y+x\left(r^3-9r^2+26r-25\right)\\ \frac{dy}{dt}& =& x+y+y\left(r^3-9r^2+26r-25\right)\end{array}$