These are animations of the system \(\dot{r}=r(r^2-3r+1),\dot{\theta }=1\) which exhibits a stable limit cycle of radius 1.

Stable limit cycle. \(\dot{r}=r(1-r^2), \dot{\theta }=1\) |
Unstable limit cycle. \(\dot{r}=-r(1-r^2), \dot{\theta }=1\) |