Pattern formation in an activator-inhibitor model: effect of albedo boundary conditions on a finite geometry

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Abstract
The authors study a piecewise linear version of an activator-inhibitor model with the aim of analysing the effect of albedo boundary conditions on the formation and stability of patterns. They find concentration profiles for both components and analyse the linear stability properties of those profiles. They show that it is possible, under certain conditions, to control the shape and the stability of the patterns. Also, a scaling behaviour on the marginal stability line has been found.