中文摘要：

讨论了一类带有毒素生产的恒化器模型，获得了模型各类平衡点存在及稳定的充要条件，通过构造Dulac函数和Lyapunov函数和运用极限系统理论，证明了该模型符合竞争排斥原理，并且得到了各类微生物绝灭的完整分析结果。

英文摘要：

A chemostat model with production of toxin is investigated, the necessary and sufficient conditions guaranteeing the existence and stability of all equilibria are found. By constructing the Dulac function and Lyapunov function, and using the theory of limit systems, the uniformity with the competitive exclusion principle is proved, and the complete results about extinction are obtained.