Pattern Formation (ii): the Turing Instability
نویسندگان
چکیده
1. Growing modes in a reaction-diffusion system In this section we summarize the classical linear Turing instability criterion for a reaction-diffusion system. Consider a reaction-diffusion system of 2-species as ∂U ∂t = ∇ · (D1 (U,V )∇U) + f (U,V ) , (1.1) ∂V ∂t = ∇ · (D2 (U,V )∇V ) + g (U,V ) , where U (x,t) ,V (x,t) are concentration for species, D1, D2 diffusion coefficients, f, g reaction terms. In this paper we consider a d-dimensional box T = (0, π) , d = 1, 2, 3, with Neumann boundary conditions for U and V , i.e.,
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