一类捕食-食饵模型的全局分歧研究

Research on global bifurcation of a predator-prey model

研究了一类具有避难所的两物种间的捕食-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,利用特征值理论得到此解的稳定性结论;利用局部分歧理论得出在(d(2j),(u*,v*))处可以产生分歧;在一维情况下,利用全局分歧理论得到由(d(2j),(u*,v*))处产生的局部分歧可以延拓成整体分歧,且连通分支jτ伸向无穷.

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. 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, it is proved that the model bifurcations at the point （d2^（j）, （u＊ ,v＊ ））. In the one dimensional case, by means of global bifurcation theory, it is proved that the local bifurcation at （d2^（j）, （u＊, v＊ ）） can be extended to global bifurcation, and the continuum τj joins up with infinity.