中文摘要：

研究一类既具有避难所又具有食饵选择的两物种间的捕食-食饵模型在第二边界条件下的平衡态正解的存在性,其功能反应函数为HollingⅡ型,给出了此解的先验估计并利用特征值理论得到此解的稳定性结论。又通过局部分歧理论,以食饵的环境容纳量k为分歧参数,给出正常数解处分歧解的具体形式。利用特征值扰动理论得出局部分歧解稳定的条件并通过全局分歧理论将其延拓到无穷。

英文摘要：

The existence of positive solutions of the steady-state system is discussed for the predator-prey model between two species with functional response Holling type Ⅱ under the second boundary conditions, in which the model has shelters and the predator is partially coupled with alternative prey. A priori-estimate of the solution is given and its stability is also discussed by means of eigenvalue theory. By means of local bifurcation theory, taking the environmental accomodation of the prey population k as a bifurcation parameter, the specific form of solutions bifurcated from the positive constant solution is given, then the condition for the local stability of bifurcation solutions is also discussed by means of eigenvalue perturbation theorem and the local bifurcation solutions can also be extended to infinite by using global bifurcation theory.