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一类具反馈控制单种群时滞模型的Hopf分支 被引量:3

Hopf Bifurcation for a Logistic Growth Model with Feedback Control and Delay
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摘要 研究了一类具有Logistic增长的单种群时滞模型,该系统受到反馈控制的影响.利用Laplace变换和其他分析技巧,得到了系统唯一正平衡态局部稳定和产生Hopf分支的充分条件. In this paper, we investigate a logistic growth feedback control model with delay and present some sufficient conditions that guarantee the stability and the existence of Hopf bifurcation.
作者 刘志军
出处 《湖北民族学院学报(自然科学版)》 CAS 2005年第3期213-215,共3页 Journal of Hubei Minzu University(Natural Science Edition)
基金 湖北省教育厅优秀中青年项目(Q200529001).
关键词 时滞 HOPF分支 反馈控制 稳定性 time delay Hopf bifurcation feedback control stability
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参考文献6

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同被引文献18

  • 1宋永利,韩茂安,魏俊杰.多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支[J].数学年刊(A辑),2004,25(6):783-790. 被引量:27
  • 2林宏康,谢向东.一类Leslie模型的定性分析[J].数学研究,1997,30(3):308-311. 被引量:2
  • 3[1]Gopalsamy K,Weng P X.Feeback Regulation Logistic Growth[J].Internet.J.Math.Sci,1993,16:177-192.
  • 4[3]Kang Y.Delay Differential Equations with Applications in Population Dynamics[M].New York:Academic Press,1993.
  • 5[4]Hassard B D,Kazararinoff N D,Wan Y H.Theory and Application of Hopf Bifurcation[M].Combridge:Combridge University,1981.
  • 6Liu Z H,Yuan R.Stability and Bifurcation in a Harvested One-predator-two-prey Model with Delays[J].Chaos Soli Frac,2006,27(5):1395-1407.
  • 7Huo H F,Li W T.Periodic solutions of delayed Leslie-Gower predator-prey model[J].Applied Mathematics and Computation,2004,155:591-605.
  • 8Song Y,Wei J.Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system[J].J Math Anal Appl,2005,301:1-21.
  • 9Freadman H I.Strea Hari Rao V.The treade-off between mutual interference and time lags in Predator-Prey System[J].Bull Math Biol,1983,45:991-1003.
  • 10Hale J K.Theory of Functional Differential Equations[M].New York:Spring,1977.

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