= Discrete-mode Turing threshold for the Brusselator
{title2=$b_T=\min_{k\ne0\ \mathrm{allowed}}[1+a^2D_u/D_v+D_uk^2+a^2/(D_vk^2)]$}
On a specified finite domain, only its boundary-compatible wavenumbers can grow. Solve the <Brusselator> mode determinant for its neutral value of $b$ and minimize over those nonzero modes. Minimizing over all continuous $k$ instead gives the usual threshold and $k_c^2=a/\sqrt{D_uD_v}$. The finite-mode minimum must still precede the homogeneous threshold to describe a <Turing instability>.
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