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Near-unity diffusivity ratio for a Turing instability

For reaction Jacobian

(- 1 1 + δ - 1 1 - δ),

the critical diffusivity ratio is

d_{c} = (\frac{2 δ + 1 + δ}{1 - δ})^{2} = 1 + 2 2 δ + O (δ) .

It approaches one as the stable reaction system approaches marginality.

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