一类非均匀Chemostat模型的共存态

Coexistence States of the Unstirred Chemostat Model

讨论了一类带有Beddington-DeAngelis型功能反应函数的非均匀Chemostat食物链模型正平衡解的存在性和稳定性以及系统解的渐近行为.首先运用极值原理、上下解和分歧理论等方法讨论了平衡态系统共存解的全局结构,给出了正解存在的充要条件;然后运用线性算子的扰动理论和分歧解的稳定性理论证明出共存解在适当条件下是稳定的;最后运用极值原理和半动力系统的一致持久性理论研究了系统解的渐近行为,得到了该系统一致持久性的条件.

The existence and stability of the positive steady-state solutions and the asymptotic behavior to the unstirred food-chain chemostat model with Beddington- DeAngelis functional response are discussed. First, by applying the maximum principle, monotone method and bifurcation theory, we discuss the global structure of the coex- istence solutions to the steady-state system. for the existence of the coexistence solutions The necessary and sufficient conditions are established. Second, some results of local stability for the coexistence solutions are obtained by the perturbation theorem for linear operators and the stability theorem for bifurcation solutions. Finally, by ap- plying the maximum principle and theory of permanence in semi-dynamical systems, we discuss the asymptotic behavior of solutions to the system, the conditions for the permanence of the system are obtained.