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研究了一类存在竞争关系的两种群微生物连续培养模型,微生物增长对营养基的消耗率参数分别取δ1(s)=A+Bs+Cs2,δ2=D+ES+Fs2.微生物增长与养料浓度之间的关系分别取为μ1(s)=m_1s2/k_1+s2,μ2(s)=m_2s2/k_2+s2.分析了系统平衡点的稳定性,运用张芷芬唯一性定理得到了系统极限环存在和唯一时,相关参数要满足的条件;用后继函数法讨论了极限环的稳定性;证明了系统存在正向不变集.
Abstract：In this paper a continuous culture model of two populations of microorganisms in the presence of competition was studied. It is assumed that the consumption rate parameters of microbial growth to the nutrient base respectively are δ1(s) = A + Bs + Cs2 and δ2= D + ES + Fs2. The relationship parameters between microbial growth and nutrient concentration respectively are μ1(s) =m_1s2/k_1+ s2 and μ2(s) =m_2s2/k_2+ s2. The stability of steady states was analysed, using Zhang Zhifen′s uniqueness theory, the existence and uniqueness of limit cycles were obtained when the parameters satisfied definite conditions. The stability of limit cycles with succeed function method was discussed. It is proved that there exists a positive invariant set.
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基本信息:
中图分类号:O175
引用信息:
[1]王永丽.微生物连续培养中一类竞争模型的定性分析[J].南通大学学报(自然科学版),2016,15(04):87-94.
2016-12-20
2016-12-20