Formation of Vegetation Patterns and Hysteresis Phenomena in Arid and Semiarid Zones

Considering the spatial effect of the complicated interactions between plant and resource (soil water) and the stochastic character of the complicated ecological processes in an ecosystem, we introduce a lattice gas model to investigate the vegetation pattern formation in the arid and the semiarid ecosystems with Monte Carlo simulations. With consistency of some previous
mean-field models, the model reproduces a wide range of patterns observed in the arid and the semiarid regions. The sequences of vegetation states are also investigated with scanning three parameters, i.e., the precipitation and the plant growth rate, and then the parameter ranges are identified where a hysteresis loop appears and two different stable states coexist. The simulation results denote that the complex structures occur only when the
precipitation parameter decreases. Moreover, based on the model, it is found that an increase of the competition of the plant for the resource along the slope direction results in the regular stripes parallel to the hill's contours. The model provides an interesting mechanism to understand the formation of the other regular vegetation stripe in a limited resource condition.