Dynamics of a vegetation management model with seasonal rainfall and groundwater diffusion

Based on reasonable management of vegetation in arid area, we consider the effect of artificial irrigation and proposed a vegetation management model with seasonal rainfall and groundwater diffusion. In this work, we describe the relationship between vegetation and groundwater by impulsive differential equation. Sufficient conditions are derived to ensure global asymptotic stability of the vegetation-extinction boundary periodic solution. Sufficient conditions are also derived to examine the permanence of the investigated system. Besides, the correctness of our results is further verified through numerical simulations. These results show that artificial irrigation and groundwater diffusion have a positive effect on the survival of vegetation in arid area.