具有非线性交叉扩散的B-D型捕食-食饵系统的共存解

Coexistence Solutions of B-D Type Predator-PreySystem with Nonlinear Cross-Diffusion

考虑一类齐次Dirichlet边界条件下具有非线性交叉扩散的B-D型捕食-食饵系统的稳态解.首先,根据线性算子的谱理论分析平凡解和半平凡解的稳定性;其次,利用正锥中的不动点指数理论给出共存解存在的充分条件.

We considered the steady-state solutions of a B-D type predator-prey system with nonlinear cross-diffusion under homogeneous Dirichlet bound ary 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 existenc e of coexistence solutions were obtained by using the fixed point index theory in positive cones.