摘要
研究了两捕食者均具有Machaelis-Menten型功能性反应,两食饵具有竞争关系的捕食系统,利用比较定理,得到了系统持久生存的充分条件,通过构造Liapunov函数,给出了系统全局渐近稳定的充分条件.此外,当系统是周期系统时,得到了系统正周期解存在唯一且全局渐近稳定的充分条件.最后,通过数值模拟来验证结论的正确性.
In this article, a two-predator-and-two competitive-prey system with MachaelisMenten Functional Response for the predator is investigated. Using comparison theorem, the permanence of the system is obtained. The sufficient conditions for the global asymptotic stability of the system are presented through constructing a Liapunov function. Further, for the periodic case, a set of sufficient conditions is proved, which guarantee the existence, uniqueness and global asymptotic stability of a positive periodic solution. Numerical simulation illustrate the feasible of the main result.
作者
梁桂珍
宋鸽
LIANG Gui-zhen;SONG Ge(Department of Mathematics and Information Science,Xinxiang Univesity,Xinxiang 453003,China;Department of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450000,China)
出处
《数学的实践与认识》
北大核心
2018年第21期290-296,共7页
Mathematics in Practice and Theory
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)
