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- W2013172036 abstract "The interesting paper entitled Limit Cycle Oscillations in Compartmental Chemical Systems by Glass and Perez, 1 suggested to us the following remarks. In the discussion section of this paper it is stated that the symmetry breaking instabilities analyzed in the works by Turing2 and Lefever3 require unequal diffusion coefficients. A similar conclusion has already appeared in a work by Edelstein4 who has analyzed symmetry breaking instabilities leading from homogeneous to spatially organized states for a general reaction-diffusion system involving two variables. In this note we want to emphasize that recent investigations of nonlinear chemical kinetics have brought out the influence of the boundary conditions on the solutions of the nonlinear partial differential equations. For unbounded media or for periodic boundary conditions-which have been adopted in Turing's model as well as in earlier analysis of the trimolecular scheme3-space dependent solutions induced by diffusion do indeed only arise for unequal diffusion coefficients. For, in the case of equal diffusion coefficients, the first bifurcation from the uniform steady state solution leads necessarily to a uniform solution like, e. g., a limit cycle. However, for other boundary conditions the situation can be very different. (1) An analysis of the trimolecular scheme in a onedimension space, in the case where the concentrations are held fixed and equal to their uniform steady state values at the boundaries," @default.
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- W2013172036 date "1976-02-01" @default.
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- W2013172036 title "Some comments on the role of the diffusion coefficients in the onset of spatial and spatiotemporal patterns" @default.
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- W2013172036 doi "https://doi.org/10.1063/1.432281" @default.
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