Positive steady state solutions of a plant-pollinator model with diffusion

Abstract

In this paper, a plant-pollinator population system with diffusion is investigated, which is described bya cooperative model with B-D functional response.Using the Leray-Schauder degree theory, we discuss the existence of positive steady state solutions of the model.The result shows when the growth rate of plants is large and the death rate of pollinators is small,the plants and pollinators can coexist.By the regular perturbation theorem and monotone dynamical system theory,the uniqueness and stability of positive solutions have been studied.Especially, we show that the unique positive solution is a global attractor under some conditions.Furthermore, we present some numerical simulations, which is not only to check our theoretical resultsbut also to supply some conjectures out of theoretical analysis.