DESERTIFICATION DUE TO OVERGRAZING IN A DYNAMIC VEGETATION-SAND-GRAZER SYSTEM

A dynamic vegetation-sand-grazer model is proposed in this research, to study the effects of different grazing intensities on the growth of vegetation in arid and semi-arid areas. The model is established on the basis of three processes: the growth of vegetation, the deposition of aeolian sand, and the growth of grazers (some herbivores). The equilibrium of the model is obtained through stability analysis and this reveals that vegetation can survive in an environment of both sand burial and grazers. But we all know that overgrazing will cause desertification. Therefore numerical simulations are carried out to quantitatively demonstrate the variations of the equilibrium along with different grazing intensities and the relationships between grazing intensity and the three variables of vegetation cover, aeolian sand and grazers. During stability analysis and simulation, we obtain several critical points of the vegetation-sand-grazer system, such as grazers bringing in point, point of maximum volume of grazers, Hopf bifurcation point and the initial grazers with respect to the projection of separatrix on vegetation-aeolian sand plane. And based on these critical points, the process of desertification can be divided into four stages: healthy (no grazing and moderate grazing), passive desertification, active desertification (overgrazing), and ecosystem collapse. The new perspective in this research may promote the understanding of desertification process and may also provide useful information for the management of graziery.