一类具有毒素的非均匀chemostat模型正解的存在性和唯一性  

Existence and Uniqueness of Positive Solutions to an Unstirred Chemostat with Toxins

作　　者：李海侠 Li Haixia(Institute of Mathematics and Information Science,Baoji University of Arts and Sciences,Shaanxi Baoji 721013)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《数学物理学报（A辑）》2020年第5期1175-1185,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801013);陕西省自然科学基础研究计划项目(2014JQ2-1003);宝鸡市科技计划项目(2018JH-20);宝鸡文理学院博士科研项目(ZK2018069)。

摘　　要：研究了一类具有毒素的非均匀chemostat食物链模型.运用稳定性理论分析了平凡解和半平凡解的稳定性,并采用最大值原理和上下解方法给出了正解的先验估计.接着,利用不动点指数理论得到了正解存在的充分条件.最后,通过扰动理论和分歧理论讨论了毒素对动力学行为的影响,得到正解的稳定性和唯一性.结果表明毒素存在时,当微生物u和v的生长率较大时物种能共存.进而当毒素的影响充分大且微生物v的生长率介于一定范围内时系统存在唯一且稳定的正解.A food chain model in the unstirred chemostat with toxins is studied.The stability of the trivial solution and semi-trivial solution is analyzed by means of the stability theory,and a priori estimate of positive solution is given by the maximum principle and the super and sub-solution method.Then,by using the fixed point index theory,the sufficient conditions for the existence of positive solutions are achieved.Finally,the effect of the toxins on the dynamic behavior is discussed by virtue of the perturbation theory and bifurcation theory,and the stability and uniqueness of positive solutions are obtained.The results show that the species can coexist when the growth rates of the microorganisms u and v are larger in the presence of the toxins.Furthermore,if the effect of the toxins is sufficiently large,the system has unique stable positive solution when the growth rate of the microorganism v belongs to a certain range.

关 键 词：CHEMOSTAT模型 毒素 不动点指数理论 分歧理论 扰动理论 唯一性 

分 类 号：O175.26[理学—数学]