一类捕食-食饵模型渐近稳定性分析  

Asymptotic stability analysis of a predator-prey model

作　　者：洪泽澎 王治国[1] HONG Zepeng;WANG Zhiguo(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,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：《纺织高校基础科学学报》2020年第1期81-87,共7页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(61672021)。

摘　　要：为研究生物体死亡率对恒化器中物种存活、灭绝的影响,提出一种具有死亡率的捕食-食饵恒化器模型。考虑模型常数平衡解的稳定性,得到了平衡解渐近稳定的充分条件。借助一致持久和比较原理研究系统的长时行为,给出了在具有死亡率的恒化器中物种持续生存的培养策略。利用数值模拟进一步论证了所得结果的有效性。In order to investigate the effect of the mortality of organism on the survival and extinction of species in the chemostat,a predator-prey chemostat model with mortality was proposed.Considering the stability of the constant equilibrium solution of the model,a sufficient condition for the asymptotic stability of the equilibrium solution is obtained.The long-term behavior of the system was studied by means of uniform persistence and comparison principles,and finally the culture strategy of species persistence in the chemostat with mortality was given.The validity of the results are further demonstrated by numerical simulation.

关 键 词：恒化器 稳定性 一致持久 数值模拟 

分 类 号：O175.13[理学—数学]