Abstract
In this paper, we consider the global behaviors of Monod type chemostat model with nutrient recycling and impulsive input. By introducing a new study method, the sufficient and necessary conditions on the permanence and extinction of the microorganisms are obtained. Furthermore, by using the Liapunov function method, the sufficient condition on the global attractivity of the system is established. Lastly, an example is given, the numerical simulation shows that if only the system is permanent, then it also is globally attractive.
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