摘要
研究了具有Allee效应和反馈控制的单种群Logistic模型的动力学行为.首先对此模型边界平衡点的局部稳定性时做了进一步修正,证明了边界平衡点在正平衡点存在时是鞍结点,但正平衡点不存在时却是一个稳定结点.其次证明了正平衡点全局渐近稳定的充分条件以及Hopf分支和极限环的存在性.结论说明Allee效应和反馈控制使得系统变得不稳定,种群密度随着Allee效应的增大而降低直至绝灭.最后用数值模拟证明结论的正确性.
It study the dynamic behavior of the single species logistic model with Allee effect and feedback control in this paper.Firstly a mistake about the local stability of the trivial equilibrium is corrected,and we prove that the trivial equilibrium is a saddle-node if there exists a positive equilibrium while it is a stable-node if there is no positive equilibrium.Then we show the sufficient condition for the positive equilibrium to be global asymptotically stable,and a Hopf bifurcation occurs around the positive equilibrium,therefore there is at least a limit cycle exists around the positive equilibrium.The result shows that Allee effect and feedback control makes the system to become“unstable”,and the population density decreases as the Allee effect increases until extinction.Finally,numerical simulations are conducted to confirm the conclusion.
作者
方侃
陈晓英
FANG Kan;CHEN Xiaoying(Fuzhou University Zhicheng College,Fuzhou,Fujian 350001,China)
出处
《闽南师范大学学报（自然科学版）》
2021年第3期39-45,共7页
Journal of Minnan Normal University：Natural Science
基金
福建省教育厅中青年教师教育科研项目(JT180805)
福建省自然科学基金面上项目(2019J01651)。
