The Qualitative Analysis Of The Chemostat Systems

Abstract On the condition of a food chain in which two microbes are cultivated continuously we consider two kinds of Chemostat models. One of them is that γ1(S) and γ2(x) are metabolized Monod type, and the other is that γ1(s) ismetabolized type and γ2(x) is Monod type .In any of the cases, we prove that theChemostat system has an unique periodic solution being stable globally, and discuss the stability of the positive equilibrium in the 3-dimension space .