ABSTRACT
The development of spontaneous stationary vegetative patterns in an arid flat environment is investigated by means of a hexagonal planform nonlinear diffusive instability analysis applied to the appropriate model system for this phenomenon. In particular, that process can be modeled by a partial differential interaction-diffusion equation system for the plant biomass density and the surface water content defined on an unbounded flat spatial domain. The main results of this analysis can be represented by closed-form plots in the rate of precipitation versus the specific rate of plant density loss parameter space. From these plots, regions corresponding to bare ground and vegetative patterns consisting of parallel stripes, labyrinth-like mazes, hexagonal arrays of gaps, irregular mosaics, and homogeneous distributions of vegetation, respectively, may be identified in this parameter space. In addition, by performing a square-planform nonlinear stability analysis on this governing system, it is shown that no such checkerboard patterns are stable. Then, those theoretical predictions are compared with both relevant observational evidence involving tiger and pearled bush patterns and existing numerical simulations of related differential flow instability nonlinear model systems, appropriate for vegetative pattern formation on hillsides.
