Effects of feedback regulation on vegetation patterns in semi-arid environments

It is well known that vegetation patterns characterize the distribution of the vegetation and provide some signs for vegetation protection. The positive feedbacks regulation between the water and plant biomass play an important role in the vegetation patterns in semi-arid environments, yet its influence on vegetation patterns is far from being well understood. In order to reveal a mechanism of positive feedbacks on pattern formation, a water-biomass model in semi-arid environments with soil-water diffusion feedback is presented. Our results reveal that, as the soil-water diffusion intensity decreases, the pattern transitions: gap patterns  →  stripe (labyrinth) patterns  →  spot patterns emerge. More importantly, when the soil-water diffusion feedback intensity is smaller, the feedback will promote the growth of the vegetation; when the feedback intensity is much larger, the vegetation biomass will decrease and the feedback may induce the emergence of desertification. Additionally, the rainfall can also induce the pattern transition. As the rainfall capacity decreases, the vegetation disappears and becomes the bare soil state. Our findings highlight the relationship among feedback intensity, rainfall and pattern dynamics of the vegetation.