Abstract: Based on the methods of the bifurcation theory, the degree theory and the maximum principle, a class of ratio-
dependent Holling-Leslie type predator-prey model is investigated. Then, based on treating [d2]as bifurcation parameter, the existence of positive steady-state solution is derived mainly by using the global bifurcation theory. Also, the local bifurcation can be extended to global bifurcation. Moreover, the fact that the global bifurcation joins up with infinity in the case of one-dimension is obtained.

Key words: fixed-point index, bifurcation theory, degree theory

摘要： 研究了一类基于比率依赖的Holling-Leslie捕食-食饵模型。利用分歧理论和度理论结合极值原理，以[d2]为分歧参数，得到了系统非常正解的存在性；同时得出局部分歧可以延拓到整体分歧，并给出了一维情况下整体分歧的性态。

关键词: 不动点指标, 分歧理论, 度理论