For slowly varying heterogeneity and small diffusion, a reaction-diffusion system forms localized Turing patterns precisely where the pointwise classical Turing inequalities hold.
Woolley, Visions of mathematics, chapter 48: Mighty morphogenesis (2014)
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From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ
For slowly varying heterogeneity and small diffusion, a reaction-diffusion system forms localized Turing patterns precisely where the pointwise classical Turing inequalities hold.