Turing's Diffusion-Driven-Instability Revisited-from a view point of global structure of solution sets

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To explain how a spatial structure is autonomously formed in the embryogenesis, Turing proposed the notion of "Diffusion-Driven-Instability" (DDI, for short), which says that when two chemicals with different diffusion rates react each other, spatially homogeneous states may be destabilized and nontrivial spatial structure emerges as a result. Mathematically, this is considered as bifurcation of nonconstant steady-state solutions from a constant stationary solution. In this project we showed patterns can be formed without bifurcation from a constant stationary solution, and proposed a new interpretation of Turing's DDI.