In this paper, we investigate a mode selection problem for the Turing patterns generated from small random initial disturbances in one-dimensional reaction-diffusion systems on a sufficiently large domain. For this problem, it is widely accepted that the maximizer of the dispersion relation give rise to the wavenumber to be selected. Even in a small neighborhood of the bifurcation point, our numerical experiments show that this is not always true.
"Deviation from the Predicted Wavenumber in a Mode Selection Problem for the Turing Patterns." Japan J. Indust. Appl. Math. 25 (3) 281 - 303, October 2008.