具反馈控制的单方不能独立生存合作系统稳定性研究  

On the Stability Property of an Obligate Lotka-Volterra Mutualism Model with Feedback Controls

作　　者：周晓燕[1] 普丽琼 薛亚龙[3] 谢向东[3] 

机构地区：[1]福州职业技术学院公共基础部,福州350108 [2]福州大学数学与计算机科学学院,福州350108 [3]宁德师范学院数学系,宁德352100

出　　处：《应用数学学报》2016年第2期298-305,共8页Acta Mathematicae Applicatae Sinica

基　　金：福建省自然科学基金(2015J01012;2015J01019)资助项目

摘　　要：研究具有反馈控制的单方不能独立生存两种群合作系统正平衡点和边界平衡点的稳定性.通过构造适当的Ly印unov函数分别得到一组保证正平衡点和边界平衡点全局吸引的充分性条件.我们的结果表明在原系统存在唯一的全局吸引的正平衡点时,反馈控制变量控制在一定的范围,则所研究系统仍然具有唯一的全局吸引的正平衡点;反馈控制变量足够大,则第二个种群将最终绝灭;在原系统只有一个全局稳定的边界平衡点时,反馈控制变量仅改变正平衡点的位置,而不会改变边界平衡点的稳定性.A two species obligate Lotkn-Volterra mutualism model with feedback controls is studied in this paper. By constructing suitable Lyapunov functions, sufficient condition which guarantee the global attractivity of the positive equilibrium and boundary equilibrium are obtained, respectively. Our results show that if the system without feedback controls admits a unique positive equilibrium, then restrict the feedback control variables to some range, the stability property of the positive equilibrium still retains, however, if the feedback control variables are enough large, then the boundary equilibrium become globally stable, which means the extinction of second species; If the system without feedback controls admits a unique globally stable boundary equilibrium, then feedback control variables can only influence the position of the equilibrium, and have no influence on the stability of the equilibrium.

关 键 词：合作系统 反馈控制 LYAPUNOV函数 全局吸引性 

分 类 号：O175.14[理学—数学]