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The polar equations areEvery positive zero of the radial factor is therefore a circular periodic orbit of period $2\pi$. Writing $s=r^2$, the equation isThe resulting count isFor the two-orbit range, $s_{-}<\lambda /2<s_{+}$. Differentiating the radial vector field at an orbit givesso the inner orbit is unstable and the outer orbit is stable. Atthey meet in a saddle-node bifurcation of periodic orbits. Atthe inner orbit shrinks into the origin, giving the second bifurcation.