非均匀Chemostat竞争模型的共存态  

Coexistence States for the Competition Model in the Unstirred Chemostat

作　　者：李海侠[1,2] 郑秋红[3] 李艳玲[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062 [2]宝鸡文理学院数学系,宝鸡721013 [3]浙江万里学院,宁波315100

出　　处：《工程数学学报》2012年第6期883-888,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10971124);陕西省教育厅科研计划资助项目(12JK0856);陕西省科技新星专项项目(2011kjxx12);宝鸡文理学院重点基金(ZK11128)~~

摘　　要：本文讨论了一类质粒载体的微生物与质粒自由的微生物竞争的非均匀Chemostat模型.利用极值原理以及Hopf边界引理给出了正平衡解的先验估计,然后利用锥映象不动点指数理论、算子谱分析以及局部分歧理论得到了正平衡解存在的充分条件,最后运用线性算子的扰动理论和分歧解的稳定性理论判定了局部分歧解的稳定性.研究结果表明,当参数满足一定条件时,两竞争物种能够共存.Investigated in this paper is a competition model between plasmid-bearing and plasmid-free organisms in the unstirred Chemostat. The priori estimates of the positive steady-state solutions are given by applying the maximum principle and Hopf boundary lemma. Then the sufficient conditions for the existence of positive steady-state solutions are obtained by using the fixed point index theory in cone, the spectrum analysis of operators and the local bifurcation theory. Finally, the stability of the local bifurcation solutions is established by the perturbation theorem for linear operators and the stability theorem for bifurcation solutions. Our results show that, when the parameters satisfy certain conditions, two species will coexist.

关 键 词：CHEMOSTAT模型 极值原理 不动点指数 分歧 稳定性 

分 类 号：O175.26[理学—数学]