= Brusselator Turing-before-Hopf diffusivity condition
{c}
{title2=$D_v/D_u>((\sqrt{1+a^2}+1)/a)^2$}
For the <Brusselator>, the stationary spatial threshold is $b_T=(1+a\sqrt{D_u/D_v})^2$ and the homogeneous oscillatory threshold is $b_H=1+a^2$. A genuine <Turing instability> appears first only if $b_T<b_H$, which rearranges to the displayed diffusivity-ratio bound. Equality gives simultaneous stationary spatial and homogeneous oscillatory neutral modes. Otherwise homogeneous loss of stability occurs first.
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