一类具有交叉扩散的捕食-食饵模型的共存性

Coexistence for a predator-prey model with cross-diffusion

讨论了一类新型的具有交叉扩散项的捕食-食饵模型非常数正解的存在性。首先,给出了正解的先验估计;其次,利用度理论得到非常数正解的存在性。结果表明:对于给定的交叉扩散系数,当捕食者与食饵的增长率控制在一定范围内时,两物种可以共存。

The existence of non constant positive solutions for a new predator prey model with cross diffusion is studied.Firstly,a priori estimate of positive solutions is given.Then,the existence of non constant positive solutions is given by using degree theory.The result shows that for fixed cross diffusion coefficients,the predator and prey can coexist when the growth rates of them are controlled in a certain range.