中文摘要：

研究一类在Dirichlet边界条件下带有广义HollingⅢ型功能反应项的修正型Leslie捕食-食饵模型.通过以c为分歧参数,利用极值原理、分歧理论和稳定性理论,得到平衡态正解的局部存在性和稳定性.并且进一步分析了局部分歧解的全局走向,得出(u(s),v(s))可以沿参数c延拓为全局分支解.

英文摘要：

A predator-prey system of modified Leslie type with the generalized Holling type Ⅲfunctional response under Dirichlet boundary conditions is studied.The local existence and sta-bility condition of positive solutions are given by regarding c as a bifurcation parameter and making use of maximum principle,bifurcation theory and stability theory.Furthermore,the global structure of local bifurcation solutions is investigated.