Dynamics Of Cyclic Competition System

Biodiversity is important to the viability of ecological systems. Biodiversity in ecosystems is promoted by cyclic, nonhierarchical interactions among competing species. Main features of such non-transitive relations are described by the rock–paper–scissors game, where rock crushes scissors, scissors cut paper, and paper outperforms rock in turn. In combination with spatial dispersal of populations, this type of competition leads to the stable coexistence of all species and the maintenance of biodiversity. However, population mobility, spatial dispersal, hierarchy and fluctuation are some central feature of real ecosystems. Here, we observe the influence of these features on biodiversity.In this paper we stated the cyclic competition stochastic theory and SSA, the influence of populations on the biodiversity,'zero-one'survival law in rock-scissors-papers system, the effect of different spatial dispersal on biodiversity, the influence of species'intelligence on competition, and so on; and at last we investigate the behavior of hierarchy in cyclic system, and find that phenomenon of the elimination of hierarchy in a completely cyclic competition. This is the focal point of this paper, and the author will stated it in detail in big space.