Abstract
We study the dynamics of spotted Turing patterns produced by an activator-inhibitor model on the surface of a cylinder and advected along the direction parallel to the cylinder. We show that, when the advection velocity increases, the symmetry of the regular solution is broken and the activator peaks self-organize onto spiral lattices. We consider these structures as prototypes of patterns for cylindrical phyllotaxis and suggest that they could provide a first step in the experimental realization of phyllotactic arrangement within a reaction-diffusion system.
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