具反馈控制的一方不能独立生存偏利合作系统的稳定性  

The stability of a commensal system that can′t survive independently by one party with feedback controls

作　　者：杨英钟[1] 王宽程[1] Yang Yingzhong;Wang Kuancheng(Minnan University of Science and Technology, Department of Information Management,Quanzhou 362700, China)

机构地区：[1]闽南理工学院信息管理学院,福建泉州362700

出　　处：《纯粹数学与应用数学》2018年第1期73-80,共8页Pure and Applied Mathematics

基　　金：福建省中青年教师教育科研项目(JAT170739)

摘　　要：研究具反馈控制的一方不能独立生存的两种群偏利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Lyapunov函数分别得到保证正平衡点和边界平衡点全局渐近稳定的充分性条件,并通过MATLAB进行数值模拟.研究结果表明,在原系统存在正平衡点时,适当的反馈控制变量仅改变正平衡点的位置,不会改变正平衡点的稳定性;但不适当的反馈控制变量将导致系统中不能独立生存的种群绝灭.A two species commensal symbiosis model with feedback controls is studied.By constructing a suitable Lyapunov function,the sufficient conditions for ensuring the global asymptotic stability of the positive equilibrium point and the boundary equilibrium point are obtained.And the numerical simulation is carried out through MATLAB.Research results show that if the original system has a positive equilibrium point.The suitable feedback control variables only change the position of the positive equilibrium point and do not change the stability of the positive equilibrium point.But unsuitable feedback control variables will lead to the extinction of the population that can not survive independently in the system.

关 键 词：反馈控制 偏利合作系统 LYAPUNOV函数 全局渐近稳定 

分 类 号：O175.14[理学—数学]