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中文摘要：
考察一类具有抑制剂的质体负载（plasmid-bearing）与质体自由（plasmid-free）的物种相互竞争的恒化器模型．首先，研究了全局分支的形状和正平衡态的多解性．结果表明，存在μ^＊〉0，使得如果体现抑制剂作用的参数μ〉μ^＊，则分支为次临界的，且当u的最大生长率a满足一定条件时，模型至少存在两个共存解．其次，得到了模型的一些动力学行为．采用的主要数学工具包括分歧理论，锥映射上的度理论，各种比较原理和椭圆估计．
英文摘要：
This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, the shape of global bifurcation branch and existence of multiple positive steady states are examined. It turns out that there exists μ^＊ 〉 0 such that if the parameter, which represents the effect of the inhibitor, μ 〉 μ^＊, then the bifurcation is subcritical and this model has at least two coexistence solutions provided that the maximal growth rate a of u lies in a certain range. Secondly, some dynamical behavior of this model is also established. The main mathematical approach relies on bifurcation theory, degree theory in cones, various comparison principles and elliptic estimates.
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