Distribution models of grazing animals around a grassland resource point

In this paper, the distribution of grazing animals around a resource point on a grassland was studied by using theories of stochastic process and differential equations. The results showed that grazing animals distribute in a circle with the resource point center because of the resource restriction. The population located at an arbitrary position when t = 0 would be concentrate on x = 0 as t → ∞. The limiting distribution is the normal distribution N(0,Dβ). The probabilities that animals distributed in some given concentric circles were evaluated, which could explain why changes in vegetation cover is likely to be most extensive close to the resource point and less so with increasing distances.