恒化器中微生物连续培养单食物链模型的定性分析  

Qualitative analysis for the single food chain model of microorganism continuous culture in chemostat

作　　者：刘婧[1] 杨淑芹[1] 

机构地区：[1]大连海事大学数理系,辽宁大连116026

出　　处：《大连海事大学学报》2004年第3期88-91,共4页Journal of Dalian Maritime University

基　　金：国家自然科学基金资助项目(60174014).

摘　　要：假设被捕食种群对营养基的消耗率参数为δ1(s)=A+Bs,捕食种群对被捕食种群的消耗率参数为δ2(x1)=C+Dx1,功能反应函数取Monod类型,这样可以更逼真地模拟自然环境.利用常微分方程的定性理论分析了系统平衡点的稳定性,证明了系统存在正向不变集,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的参数及环境参数之间的关系.In this paper, the qualitative behavior of the single food chain model of microorganism continuous culture in the well stirred Chemostat is studied. To simulate the natural environment more actively, We assume that the consumption rate of the nutrition basis for the preyed species is δ_1(s)=A+B(s), the consumption rate for the preying species with respect to the predator species is δ_2(x_1)=C+D(x_1) and the response function is taken as the Monod form. We analyze the stability of steady states by the qualitative theorem of the ordinary differential equation,prove that there exists a positive invariant set and obtain the relationship among the parameters of the microorganisms themselves, the coexistence of two microorganisms and the environment in the single food chain model with a variable consumption rate.

关 键 词：微生物 连续培养 恒化器 食物链模型 平衡解 平衡点的稳定性 不变区域 

分 类 号：O175.14[理学—数学]