Abstract: A prey-predator system on zooplankton is investigated under the Dirichlet boundary condition. The priori estimates of steady-state solutions are given. Based on treating b as the bifurcation parameter, the existence of positive steady-state solution is derived by the global bifurcation theory, and the local bifurcation is extended to global bifurcation. The continuum C joining up with infinity is proved.

Key words: prey-predator, upper-lower solution, global bifurcation

摘要： 主要研究一类在齐次第一边界条件下浮游植物和浮游动物的捕食-食饵模型。给出了平衡态方程解的先验估计。利用分歧理论，以b为分歧参数，得到平衡态系统正解的存在性，将局部分歧延拓为全局分歧。结果表明连通分支C延伸向无穷。

关键词: 捕食-食饵模型, 上下解方法, 全局分歧