一类带有内部存储和抑制剂的恒化器模型的共存解  

Coexistence solutions of the chemostat model with internal storage and inhibitor

作　　者：李星星 王治国[1] 李艳玲[1] LI Xing-xing;WANG Zhi-guo;LI Yan-ling(School of Mathematics and Information Science,Shaanxi Normal University,Xi an 710119,Shaanxi,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《西北师范大学学报（自然科学版）》2018年第5期16-24,共9页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61672021);陕西省自然科学基础研究计划资助项目(2014JM1003)

摘　　要：讨论一类带有内部存储和抑制剂的非均匀恒化器模型正平衡解的存在性.由于模型中比率项的奇性,导致通常的线性化方法对本模型并不适用.为克服这个困难,首先建立模型正平衡解细致的先验估计,该估计表明模型的正平衡解含于一个特殊的锥内.然后借助一类非线性特征值问题的主特征值及锥上的不动点指标理论给出了模型正平衡解存在的充分条件.结果表明当其对应的非线性特征值问题的主特征值满足一定关系时,系统至少存在一个正平衡解.The existence of positive steady state solutions for an unstirred chemostat model with internal storage and inhibitors is discussed.Due to the singularity of the ratio term in the model,the usual linearization method is not available.In order to overcome this difficulty,the priori estimates of the positive steady state solutions of the model are established firstly,which ensure that the positive steady state solutions of the model are contained within a special cone.Then,some sufficient conditions for the existence of positive steady state solutions of the model are given by using the principal eigenvalues of the nonlinear eigenvalue problems and the fixed point index theory.The results show that the system has at least one positive steady state solution when the principal eigenvalue of the nonlinear eigenvalue problem satisfies some certain conditions.

关 键 词：内部存储 抑制剂 恒化器 锥上的度理论 非线性特征值问题 

分 类 号：O175.26[理学—数学]