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Partial differential equation

Diffusion equation

Reaction-diffusion system

Turing instability

Two-species diffusion-driven instability criterion

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.


Near-unity diffusivity ratio for a Turing instability

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 14C / d / Solution

Near-unity diffusivity ratio for a Turing instability

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Near-unity diffusivity ratio for a Turing instability

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