Advection and autocatalysis as organizing principles for banded vegetation patterns

TL;DR

This paper presents a minimal reaction-diffusion model for banded vegetation patterns in semi-arid landscapes, highlighting the roles of advection and autocatalysis in pattern formation, migration, and edge dynamics.

Contribution

It introduces a novel reaction-diffusion framework with conservation laws to analyze vegetation band phenomena, providing new insights into their migration and edge interactions.

Findings

Reaction-diffusion model captures vegetation band formation

Conservation law explains band migration dynamics

Analysis reveals interplay between upper and lower edges

Abstract

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.