= Quadratic-product flow with a double-zero bifurcation
{title2=$\dot u=u(\mu+u-v),\quad\dot v=\lambda(u^2-v)$}
For $\lambda>0$, the <equilibrium points> are the origin and $(s,s^2)$ with $s=(1\pm\sqrt{1+4\mu})/2$. The nonzero branches have Jacobian trace $s-\lambda$ and determinant $\lambda s(2s-1)$. They have a <saddle-node bifurcation> at $\mu=-1/4$, $s=1/2$; the origin exchanges stability with the lower branch at the <transcritical bifurcation> $\mu=0$. A <Hopf bifurcation> occurs on the upper branch at $\mu=\lambda(\lambda-1)$ for $\lambda>1/2$. The point $(\mu,\lambda)=(-1/4,1/2)$ has a double zero <eigenvalue> and a nontrivial Jordan block. Its generic unfolding includes a saddle-loop curve and the intervening stable <periodic orbit> region.
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