关键词: 捕食-食饵系统, B-D反应函数, 稳定性, 共存解

Abstract: We considered the steady-state solutions of a B-D type predator-prey system with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, we analyzed the stability of trivial solution and semi-trivial solutions based on the spectral theory of linear operators. Secondly, the sufficient conditions for the existence of coexistence solutions were obtained by using the fixed point index theory in positive cones.

Key words: predator-prey system, B-D type response function, stability, coexistence solution