Coupling effect of grazing pressure and nutrient enrichment on system stability

A three dimensional nutrient-plant–herbivore model was proposed and conditions for boundedness, positive invariance, existence and stability of different equilibrium points, Hopf-bifurcation and global stability were obtained. We performed numerical simulations to observe the simultaneous effect of the top-down and the bottom-up mechanism on the system. It was found that nutrient enrichment destroyed the coexistence steady state of the system. This nutrient enrichment could be due to high nutrient input rate or high nutrient recycling rate. In both cases the system showed instability. Moreover, these results were independent of the grazing pressure and the predation functional form.

► A three dimensional nutrient-plant–herbivore model was proposed and analyzed.
► Nutrient enrichment destroyed the coexistence steady state of the system and cause oscillation.
► Limited or low nutrient availability may cause plant and herbivore deaths.
► Grazing pressure cannot control the system destruction due to nutrient enrichment or nutrient limitation.