Advection and autocatalysis as organizing principles for banded vegetation patterns.

We motivate and analyze a simple model for the formation of banded vegetation patterns. The model incorporates a minimal number of ingredients for vegetation growth in semi-arid landscapes. It allows for comprehensive analysis and sheds new light onto phenomena such as the migration of vegetation bands and the interplay between their upper and lower edges. The key ingredient is the formulation as a closed reaction-diffusion system, thus introducing a conservation law that both allows for analysis and provides ready intuition and understanding through analogies with characteristic speeds of propagation and shock waves.