一类具有密度制约的捕食系统极限环问题

根据生态种群动力学原理,考虑一类具有密度制约的食饵-捕食者系统,利用微分方程定性理论,对系统的正平衡点性态进行分析,同时对系统的中心-焦点型奇点的焦点量进行计算,根据Hopf分支理论讨论极限环的存在情况,并给出了正平衡点外围存在唯一极限环的充分条件,最后利用matlab软件进行数据仿真,验证所得结论的准确性.

Limit cycle problem of a predator-prey system with density dependence

According to the principle of ecological population dynamics, a class of density-dependent bait-predator system is considered. The qualitative theory of differential equation is used to analyze the positive equilibrium state of the system, and calculate the focus quantity of the Center-Focus type singularities of the system. The existence of limit cycles is discussed according to the Hopf branch theory. The sufficient conditions for the existence of a unique limit cycle outside the positive equilibrium point are given. Finally, matlab software is used for data simulation to verify the accuracy of the conclusion.