For a Selkov--Schnakenberg model as a prototype reaction-diffusion system ontwo dimensional domains we use the continuation and bifurcation softwarepde2path to numerically calculate branches of patterns embedded in patterns,for instance hexagons embedded in stripes and vice versa, with a planarinterface between the two patterns. We use the Ginzburg-Landau reduction toapproximate the locations of these branches by Maxwell points for theassociated Ginzburg-Landau system. For our basic model, some but not all ofthese branches show a snaking behaviour in parameter space, over the givencomputational domains. The (numerical) non-snaking behaviour appears to berelated to too narrow bistable ranges with rather small Ginzburg-Landau energydifferences. This claim is illustrated by a suitable generalized model. Besidesthe localized patterns with planar interfaces we also give a number of examplesof fully localized atterns over patterns, for instance hexagon patches embeddedin radial stripes, and fully localized hexagon patches over straight stripes.
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