恒化器中一类具有非常数消耗率微生物培养模型的定性分析

研究了一类具有非常数消耗率的微生物培养模型.假设被捕食种群对营养基的消耗率参数为δ1(s)=A+Bs+Cs2,捕食种群对被捕食种群的消耗率参数为δ2(x)=R+Px+Qx2,利用常微分方程的定性理论分析系统平衡点的存在性和稳定性,证明了系统存在正向不变集,并得到非常数消耗率单食物链模型中两种微生物共存与微生物本身参数、环境参数之间的关系.

Qualitative Analysis for a Class of Microbial Continuous Culturemodel with Variable Yield in Chemostat

A class of culture model with variableconsumption rate was considered.It was assumed that the consumption rate ofnutrition basis for the prayed species is δ1(s)=A+Bs+Cs2 and the consumption rate for the preying species with respect to the predatorspecies is δ2(x)=R+Px+Qx2.By the qualitative analysis ofthe culture model,the stability of steady states and the existence of a positive invariant set were discussed.The relationships among the parameters of themicroorganisms themselves,the coexistence of two microorganisms and theenvironment in the single food chain model with a variable consumption rate were presented.