一类非均匀恒化器竞争模型共存态的全局分歧

研究一类具有质载和代谢物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正平衡解的先验估计,借助特征值理论得到正平衡解存在的必要条件.以质载物种的最大增长率a为分歧参数,采用局部分歧理论构造正平衡解的局部分支,利用全局分歧理论证明了正平衡解的局部分支可延拓为全局分支,并分析解的稳定性和全局分歧解的走向.结果表明,该全局分支沿参数a延伸到无穷.从生物学角度看,当质载物种的最大增长率a∈(λ1/(1-q),+∞)时,两物种可以共存.

Global bifurcation of coexistence state for a competition model in the unstirred chemostat

Global bifurcation of a competition model between plasmid-bearing and plasmid-free organisms in the unstirred chemostat with metabolites is discussed.A priori estimates for posi-tive steady-state solutions was established by the maximum principle.Necessary conditions for the positive steady-state solutions were given by the eigenvalue theory.By using the local bifur-cation theory and regarding the growth rate of the plasmid-bearing organism a as bifurcation parameter,the local bifurcation branch of positive steady-state solutions is constructed,and it can be extended to a global solution branch by using the global bifurcation theory.Moreover, the stability of solutions and the trend of the global bifurcation solutions were analyzed.It is shown that the global solution branch extends to infinity along the parameter a .From a biolog-ical point of view,two competitors can coexist when the maximal growth rate of the plasmid-bearing organism a ∈(λ1/(1-q),+∞).