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Abstract

Turing's theory of pattern formation has been used to describe the
formation of self-organized periodic patterns in many biological,
chemical, and physical systems. However, the use of such models is
hindered by our inability to predict, in general, which pattern is
obtained from a given set of model parameters. While much is known near
the onset of the spatial instability, the mechanisms underlying pattern
selection and dynamics away from onset are much less understood. Here,
we provide physical insight into the dynamics of these systems. We find
that peaks in a Turing pattern behave as point sinks, the dynamics of
which is determined by the diffusive fluxes into them. As a result,
peaks move toward a periodic steady-state configuration that minimizes
the mass of the diffusive species. We also show that the preferred
number of peaks at the final steady state is such that this mass is
minimized Our work presents mass minimization as a potential general
principle for understanding pattern formation in reaction diffusion
systems far from onset.