The distribution models of grazing animals between two grassland resource points

In this paper, by using theories of stochastic process and differential equation, the authors systematically studied the distribution of grazing animals between two resource points and established the dispersal model that describes the animals' distribution. Its limiting distribution could describe not only the consequences of spatial pattern development for a long term, but also the processes of formation and development of animals spatial patterns by temporal variable t of stochastic process. This paper gave both the animals distribution in each circular ring with the same center, and the maximum domain of animals' distribution. Based on these studies, the intrinsic mechanisms of spatial and temporal patterns of grazing animals were discussed.