一类具有Allee效应和Beddington-DeAngelis反应的捕食者-食饵系统的稳定性

\justifying The predator-prey relationship is a typical interaction in the ecosystem. This paper mainly studies the cross-diffusion predator-prey model with Allee effect and Beddington-DeAngelis response function under homogeneous Neumann boundary conditions. The growth of prey population is affected by Allee effect, and the Beddington-DeAngelis type response function reflects the predator-prey relationship. This paper first uses the comparative principle to obtain the boundedness of the positive solution, secondly uses the linearization method to prove the stability of the equilibrium point, and finally discusses the conditions for the existence of the non-constant steady-state solution by using the Leray-Schauder degree theory.