Quick summarize...

You first have to show that there is a trapping region. Do this by setting .

=> then sub in and . Show that a disk of radius r is a trapping region by showing that r' <= 0...

Then the theorem says if there are no critical points within this trapping region (or if there is either an unstable spiral or unstable node) there will be a limit cycle (periodic solution). So just show one of those is true.