Grazing duration and intensity modulate vegetation dynamics in semi-arid ecosystems with seasonal succession

Abstract

This study investigates the impacts of grazing duration and intensity on vegetation population dynamics in semi-arid ecosystems characterized by seasonal succession. A novel piecewise periodic model is proposed, dividing the annual cycle into three distinct phases: dry season, growth period and grazing period in wet season. We derive critical thresholds for the durations of the dry season and grazing period that determine the persistence or extinction of a single vegetation species. For two competing species, we analyze how grazing parameters influence competitive outcomes, including exclusion, coexistence, and bistability. Theoretical results are supported by numerical simulations, which illustrate bifurcation diagrams and phase transitions under varying grazing regimes. Our findings provide actionable insights for sustainable grazing management in arid and semi-arid regions.