带有交叉扩散项的捕食-食饵模型的全局分歧

Global bifurcation in a predator-prey model with cross-diffusion

文章研究了一类带有交叉扩散的捕食-食饵模型在齐次Dirichlet边界条件下正解的存在性,借助Crandall-Rabinowitz分歧理论,得出局部分歧正解的存在性,并将局部分歧延拓为全局分歧,得到正解存在的充分条件,从而给出捕食者与食饵在一定条件下可以共存的结构。

The existence of positive solutions for a predator-prey model with cross-diffusion under hom- ogeneous Dirichlet boundary conditions is studied. Based on the Crandall-Rabinowitz bifurcation theory, positive solutions emanating from the semi-trivial solutions are derived. Finally, the local bifurcation solution is developed to the global one, thus obtaining the sufficient conditions of positive solutions. It is shown that the predator and the prey can coexist under certain conditions.