Impacts of the duration and intensity of grazing cycle on vegetation population dynamics in semi-arid ecosystems with seasonal succession

A novel vegetation model involving seasonal succession to distinguish the dryperiod, growth period and grazing period is proposed. The main aim is to explore the effects of duration and intensity of grazing season on the dynamic behaviors of a single vegetation population and the competitive outcomes between two competing vegetation species. The critical duration of drought period and grazing period that enable the persistence of a single vegetation population is obtained. Further, we found that both the duration andi ntensity of grazing significantly impact the competitive outcomes between two vegetation populations. Numerical examples are performed to validate our theoretical results and in particular to obtain the bifurcation diagram for the duration of dry season and grazing period.