The predation mechanism of invertebrates (e.g., Tortanus dextrilobatus) on plankton in aquatic population ecosystem is a significant research topic. In this paper, the interaction between invertebrates and plankton is simulated by a modified Leslie-Gower predator-prey model. Using the theory of reaction-diffusion equations, a priori estimate, existence, uniqueness and stability conditions of the positive steady state solution are established. Furthermore, numerical simulations are conducted to quantitatively analyze the dynamical behavior. The research shows that as long as the Allee effect constant satisfies the appropriate relationship and the growth rates of predator and prey are appropriately large, the predator and prey can not only coexist, but also the coexistence mode is unique and stable under low predation-rate. In addition, the numerical simulations show that the coexistence may be stable under high predation-rate. Meanwhile, with the increase of predation rate, the population density of predators will decrease.
A Wed, study studied this question.