Stability Analysis Of Solutions In Competition Models With Nonlocal Dispersals

Competition models with nonlocal dispersals have been widely used in biology and ecology. For two competing species, People usually have great interest in their coexistence and extinction phenomenon. Mathematically, we’ll make an analysis of the global asymp-totic stability of the competition models’static solutions to solve the problem. So, the dissertation attempts to give some characterizations for the global asymptotic stability of the nonlocal diffusion competition models’static solutions. Further more, we try to illustrate whether the two competing species will be coexistence.First of all, the global asymptotic stability of competition models is greatly decided by the local stability of the models’semi-trivial static solutions whose unique existence have been admitted, according to the relevant conclusions proved by other documents.Then, under the assumption that the dispersal kernels are symmetric, we try to find the effect of dispersal rates, interspecific competition coefficients and the spatial distribu-tion of resources on the stability of semi-trivial static solutions in the weak competition condition.We can make an analysis of the global asymptotic stability of nonlocal diffusion competition models when we have a certain understanding to the local stability of the models’semi-trivial static solutions.Biologically speaking, we eventually give some certain features to the coexistence or extinction of the two competing models.