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Nonlinear Patterns in Chemical Networks as Symmetries of Transformation Groups

Abstract The origin of a stable spatial pattern in chemical reaction systems has been traced back to symmetries characterized by one-parameter transformation groups. The chemical reaction-diffusion system of Dreitlein and Smoes served as a model for the mathematical approach. The procedure is based on the conversion of sets of partial differential equations to equivalent systems of first order in more parameters. The latter generally admit one-parameter groups, which are related to singularities observed as pattern. It is also shown how models may be constructed from Lie-algebras using the constraints of integrability.