具有线性收获比率依赖捕食系统的Hopf分支  

Hopf bifurcations in a ratio-dependent predator-prey system with linear harvesting

作　　者：崔国虎[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2010年第4期6-9,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10961017);兰州交通大学青蓝人才工程资助项目(QL-05-20A)

摘　　要：应用微分方程的定性理论与分支方法探讨一类具有线性收获和HollingⅡ比率依赖函数捕食系统的平衡点与Hopf分支.首先通过定性理论对系统奇点性态进行分析讨论,然后利用Hopf分支理论给出了系统Hopf分支的存在性、分支方向及周期解的稳定性条件.最后,给出相应的数值模拟.The Hopf bifurcations of the predator-prey system with Holling＇s typeⅡfunctional response are mainly investigated by using the qualitative theory and the method of bifurcations.First,the behaviour of equilibrium points is discussed by means of the qualitative theory,and then the existence,stability and periodic solutions of the Hopf bifurcation are obtained by Hopf bifurcation theory.Finally,numerical simulations supporting our theoretical predictions are also given.

关 键 词：捕食系统 平衡点 极限环 HOPF分支 

分 类 号：O175[理学—数学]