交叉扩散的带Michaelis-Menton型非线性收获率的捕食-食饵模型

Prey-Predator Model with Cross-Diffusion and Michaselis-Menten Type Prey Harvesting

在Dirichlet边界条件下,寻求一类交叉扩散的带Michaelis-Menton型非线性收获率捕食-食饵模型正解的存在性.利用上下解法和Crandall-Rabinowitz分歧理论,得出正解的先验估计和一类半平凡解附近局部分歧解的存在性,并将局部分歧解延拓为全局分歧解.推导结果表明:在一定条件下,该捕食模型的正解是有界的,且捕食者和食饵可共存.

The paper discusses the existence of positive solutions to a kind of predator-prey model with cross-diffusion and Miehaselis-Menten typed prey harvesting under homogeneous Dirichlet boundary conditions. By Crandall-Rabinowitz bifurcation theory, the existence of positive solutions to a local bifurcation is proved and the local bifurcation is developed to the global one, thus obtaining sufficient conditions of positive solutions, which shows that the predator and the prey coexist under certain conditions.