= Exact anisotropic radial limit cycle
{title2=$r_p(\theta)=[2-(\cos2\theta+2\sin2\theta)/5]^{-1/2}$}
For $\dot r=r[1-r^2(2-\cos2\theta)]$, $\dot\theta=2$, the substitution $w=r^{-2}$ gives $dw/d\theta+w=2-\cos2\theta$. Its positive periodic solution yields the displayed <orbit (dynamical system)>, with full planar period $\pi$. Every other solution at the same phase has $w-w_p=Ce^{-2t}$, proving uniqueness and attraction. The limiting circles $r=1/\sqrt3$ and $r=1$ give a trapping <annulus>, with tangencies at their extremal angles.
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