Near-unity diffusivity ratio for a Turing instability
= Near-unity diffusivity ratio for a Turing instability
For reaction Jacobian
$$
\begin{pmatrix}-1&-1\\1+\delta&1-\delta\end{pmatrix},
$$
the critical diffusivity ratio is
$$
d_c=
\left(
\frac{\sqrt{2\delta}+\sqrt{1+\delta}}{1-\delta}
\right)^2
=1+2\sqrt{2\delta}+O(\delta).
$$
It approaches one as the stable reaction system approaches marginality.