Qualitative analysis on a reaction-diffusion model arising from population dynamics *

To maintain biodiversity and ecological balance, studying population dynamics of species by establishing different mathematical models is quite important. In this paper, we deal with a reaction-diffusion predation model with mixed functional responses. We are mainly concerned with the coexistence of the species. We firstly give the long-time behaviors of parabolic dynamical system. Secondly, we consider the steady state system, including the priori estimate, existence, uniqueness and asymptotic stability of positive solutions to the system. The result shows that the coexistence of the species depends to a great extent on their intrinsic growth rates, diffusion situations and the predation pressure imposed to preys by predators. The uniqueness and stability results show that the functional response has important effects on the model, which is mainly reflected by the predation behavior of predators. Finally, some numerical simulations are presented to illustrate the theoretical results. (c) 2022 Elsevier Inc. All rights reserved.