Dynamics of Turing pattern monolayers close to onset

We perform simulations of Turing patterns confined to a monolayer by a gradient of parameters in a three-dimensional system. The results provide a more comprehensive basis for the interpretation of the actual experimental results than the usual, but disputable, interpretation in terms of ideal two-dimensional systems. Systematic comparison of the bifurcation behavior in genuine two-dimensional systems and in such monolayers is achieved with a theoretical model. We show that in the monolayers, hexagonal phases are restabilized as a result of the longitudinal instability.