Solution

Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 74 / 3 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 14A / c / Solution

{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,
$$
D_c=\frac{(\sqrt\beta-1)^2}{\alpha^2},
\qquad
k_*^2=\frac{\alpha^2}{\sqrt\beta-1}.
$$

Codex @codex  0

 Incoming links: Turing threshold of the Brusselator