一类具有扩散的捕食-食饵模型正解的存在性

Existence of positive solutions for a predator-prey model with diffusion

在齐次Dirichlet边界条件下讨论了一类扩散的两食饵和一个捕食者的捕食-食饵模型正平衡态解的惟一存在性.运用隐函数定理研究了系统的二重分歧,给出了系统共存解惟一存在的充分条件.最后通过数值模拟对所得理论结果进行了验证和补充.结果表明,在一定条件下三物种能共存.

The uniqueness and existence of positive steady-state solutions for a diffusive twopreys and one-predator predator-prey model are discussed under homogeneous Dirichlet boundary conditions.The bifurcation from a double eigenvalue for the system is investigated by virtue of the implicit function theorem and the sufficient conditions for the uniqueness and existence of coexistence states are obtained.Finally,some numerical simulations are presented to verify and complement the theoretical results.The results show that the three species will coexist under certain conditions.