Pattern selection in the generalized Swift-Hohenberg model

The competition between patterns of different symmetries is studied for the generalized Swift-Hohenberg model in the presence of a large quadratic coupling in one dimension (1D) and 2D. It is shown that hexagons with different phase relations may coexist for some values of the control parameter. Numerical experiments exhibiting the effects of linear spatial ramps of the control parameter on this selection are presented. The analogy with recent patterns obtained experimentally in open chemical reactors is also discussed.