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一类具有食饵-捕食的Chemostat模型研究

发表时间:2013-07-15  浏览量:1470  下载量:388
全部作者: 荣韶虹,张娟
作者单位: 华北电力大学数理学院
摘 要: 恒化器(Chemostat)模型是一类重要的生物学模型,在生物生态研究中具有重大意义。建立具有第三类Holling功能性反应函数的食饵-捕食的Chemstat模型,利用稳定性方法理论对模型进行定性分析,得到模型可行平衡点的存在性,并通过Liyapunov函数、Jacobi矩阵等方法证明可行平衡点的全局稳定性。模型分析结果显示了食饵-捕食者一致生存、食饵生存捕食者灭绝及捕食者生存食饵灭绝的条件。
关 键 词: 常微分方程;恒化器模型;全局稳定性;平衡点;食饵-捕食
Title: Research on one Chemostat model with predator-prey populations
Author: RONG Shaohong, ZHANG Juan
Organization: Mathematics and Physics Department, North China Electric Power University
Abstract: Chemostat model is a kind of important biology model and plays a key role in the biological and ecological study. In this paper, the Chemostat model of the predator and prey populations with the Holling III reaction function was constructed. Through qualitative analysis on this model using the stability theory and method, the feasible equilibrium point of the model was obtained. In addition, the global stability of equilibrium point was proved through Liyapunov function and Jacobi matrix. Model analysis results showed the conditions that the predator and prey population was permanently survival, prey population was survial with predator population’s extinction and predator population was survial with prey population’s extinction.
Key words: ordinary differential equation; Chemostat model; global stability; equilibrium point; predator-prey
发表期数: 2013年7月第13期
引用格式: 荣韶虹,张娟. 一类具有食饵-捕食的Chemostat模型研究[J]. 中国科技论文在线精品论文,2013,6(13):1198-1203.
 
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