Turing threshold of the Brusselator
= Turing threshold of the Brusselator
{c}
When $u$ and $v$ have diffusivities $D$ and $1$, respectively, and the homogeneous Brusselator equilibrium is stable, a <Turing instability> occurs precisely when
$$
\beta>(1+\alpha\sqrt D)^2.
$$
At onset,
$$
D_c=\frac{(\sqrt\beta-1)^2}{\alpha^2},
\qquad
k_*^2=\frac{\alpha^2}{\sqrt\beta-1}.
$$