MATHEMATICAL MODELS OF VEGETATION PATTERN FORMATION IN ECOHYDROLOGY

Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation. Patterns that are induced neither by heterogeneity in soil properties nor by the local topography are generally explained as the result of spatial self-organization resulting from "symmetry-breaking instability'' in nonlinear systems. In this case, the spatial dynamics are able to destabilize the homogeneous state of the system, leading to the emergence of stable heterogeneous configurations. Both deterministic and stochastic mechanisms may explain the self-organized vegetation patterns observed in nature. After an extensive analysis of deterministic theories, we review noise-induced mechanisms of pattern formation and provide some examples of applications relevant to the environmental sciences.