基于比率且具有Machaelis-Menten型功能性反应的非自治扩散系统的持久生存  

The Permanence for a Ratio-dependent Nonautonomous System with Machaelis-Menten Functional Response and Diffusion

作　　者：梁桂珍[1] 宋鸽[1,2] 

机构地区：[1]新乡学院数学与信息科学学院,河南新乡453003 [2]郑州大学数学与统计学院,郑州450001

出　　处：《新乡学院学报》2016年第12期1-4,36,共5页Journal of Xinxiang University

基　　金：河南省科技厅科技攻关项目(132102310482);河南省高等学校重点科研项目(16A110021);新乡学院科技创新项目(12ZB17)

摘　　要：研究了一类基于比率和具有Machaelis-Menten型功能性反应的非自治扩散捕食-被捕食动力学系统,通过比较定理得到了该系统一致持久生存的充分条件。当系统是周期系统时,通过构造Liapunov泛函得到了该系统有唯一的全局渐近稳定正周期解的充分条件。A kind of ratio-dependent nonautonomous diffusion predator-prey system with Machaelis-Menten functional response was established in this paper, and the sufficient conditions for the persistence of this system were obtained by comparison theorem. When the system was periodic, sufficient conditions that ensure the existence, uniqueness, global asymptotic stability and positive periodic solution of this system were obtained by constructing a Liapunov function.

关 键 词：扩散 Machaelis-Menten型功能性反应 捕食系统 持久性 全局渐近稳定 

分 类 号：O175.21[理学—数学]