$$x' = -y + x(1-2x^2 - 3y^2)$$ $$y' = x + y(1-2x^2 - 3y^2)$$
I've started by converting to polar coordinates $$x=rcos\theta \quad y = rsin\theta, \quad rr'=xx'+yy'$$ This gives me $$r' = 1-2r^2cos^2\theta-3r^2sin^2\theta$$.
I'm not sure where to go from here to show that I've got a limit cycle. Any help would be appreciated!