污染环境中微生物培养模型的分析

Analysis of Chemostat Model with Pulsed Input in a Polluted Environment

恒化器是一个简单易于采用的用来培养微生物的实验装置。它被用做研究微生物的增长并有着对参数易于测量的优点。但是,关于恒化器模型的研究大都忽略了环境污染的情况。因此,本文考察在污染的环境中脉冲输入营养基Monod-Haldane恒化器模型.应用Floquet乘子理论和脉冲微分比较定理,得到微生物灭绝周期解是全局渐近稳定的充分条件,这意味着微生物培养失败。同时,得到在污染环境中微生物培养成功的条件,也就是系统持续生存的条件。最后讨论污染的环境对微生物培养的影响。

The chemostat is a simple and well-adopted laboratory apparatus used to culture microorganisms. It can be used to in- vestigate microbial growth and has the advantage that parameter- sare easily measurable. However, existing theories on ehemostat model largely ignore effects of the environmental pollution. Therefore, in this paper, we consider a Monod-Haldane chemo- star model with with pulsed input in a polluted environment. By using the Floquet theorem and comparison theory of impulsive differential equation, we obtain the sufficient conditions for the global asymptotical stability of microorganism-extinction periodic solution. Which shows the population of m icroorganisms will be eventually extinct. In the same time, we proved that the system is permanent under appropriate conditions on the polluted environ- ment. In this case, the microorganism is obtained. Finally, we discuss the effects of the polluted environment on the culture of microorganisms.