Positive steady state solutions of a plant-pollinator model with diffusion (Q256886)

The paper studies existence, uniqueness and stability of a positive steady state for a plant-pollinator reaction-diffusion system of cooperative type involving a Beddington-DeAngelis nonlinearity and homogeneous Dirichlet boundary conditions.NEWLINENEWLINEThe authors provide necessary conditions on the parameters of the model for the existence of positive steady states and they establish some a priori bounds, which allow them to give, by means of degree theory, (more restrictive) sufficient conditions for existence. Such a positive steady state is also shown to be unique, stable and a global attractor for the dynamics, provided that a parameter \(\alpha>0\), which takes into account the plants' efficiency in translating plant-pollinator interactions into fitness, is small.NEWLINENEWLINEFinally, some numerical simulations are presented, which on the one hand confirm the analytical results and on the other one show that the existence of a positive steady state should hold under more general conditions than the ones considered in the paper.