一类恒化器竞争模型共存态的全局分歧  

Global Bifurcation of Coexistence State for a Competition Model in the Chemostat

作　　者：刘继远[1] 聂华[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2013年第6期815-824,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11001160);陕西省科技计划项目(2011JQ1015)~~

摘　　要：研究了一类带Ivlev型反应函数的非均匀恒化器竞争模型的全局分歧.利用最大值原理获得了共存解的先验估计,借助于特征值理论、上下解方法得到了共存解存在的必要条件,采用局部分歧理论构造了共存解的局部分支,并运用全局分歧理论证明了共存解的局部分支可延拓为全局分支.结果表明该全局分支连接了模型的两半平凡解分支.从生物学角度看,当两竞争物种的最大生长率满足一定条件时,两物种可以共存.We study the global bifurcation of coexistence solutions of a competition model in the unmixed chemostat with the Ivlev type response function. A priori estimates for co- existence solutions are established by the maximum principle. Necessary conditions for the existence of coexistence solutions are given by the eigenvalue theory and the upper and lower solution method. The local bifurcation branch of positive solutions is constructed by the local bifurcation theory, which can be extended to a global solution branch by using the global bi- furcation theory. Moreover, the global solution branch connects the two semi-trivial solution branches of the model. From a biological point of view, two competitors can coexist when their maximal growth rates are within a certain re^ion.

关 键 词：恒化器 Ivlev反应函数 最大值原理 共存解 全局分歧 

分 类 号：O175.26[理学—数学]