关于具有二次相关性收获率的捕食与被捕食系统极限环的存在性分析  

Existence of limit cycle of a predatory-prey system with the harvesting rates of quadratic correlation

作　　者：卢克英[1] 窦霁虹[1] 仲文林 李鹏[1] 

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2015年第4期414-421,共8页Pure and Applied Mathematics

基　　金：陕西省教育厅自然科学专项基金(206030001);研究生自主创新资助项目(YZZ14083)

摘　　要：讨论了一类两种群具有二次相关性收获率的捕食与被捕食系统,利用常微分定性方法和分支理论,得到了系统平衡点处的性态和极限环的存在性条件,并用Matlab软件对其进行数值模拟,推广了相关文献中两种群捕食模型定性分析的相应结论.A predatory-prey system with the harvesting rates of quadratic correlation is discussed. Using the qualitative methods of ordinary differential and bifurcation theory to get the conclusions about the state of system equilibrium point, conditions for the existence of limit cycles and carries on the numerical simulation through the software. This paper is a generalization of the related literature about analysis of two species predatory-prey model qualitative.

关 键 词：Poincare切性曲线法 平衡点 HOPF分支 极限环 

分 类 号：O175.12[理学—数学]