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多时滞合作系统的稳定性与全局Hopf分支 被引量：8

Stability and Global Hopf Bifurcation for a Cooperative System with Two Delays
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摘要 以时滞为参数,研究了一类多时滞合作系统的正平衡点的稳定性及局部Hopf分支的存在性.在此基础上结合一般泛函微分方程的全局Hopf分支定理,讨论了该系统全局Hopf分支的存在性. This paper consider the stability and local Hopf bifurcation for a cooperative system when rate τ regarding as a parameter,combing the global Hopf bifurcation theorem for general functional differential equations,and we investigate the existence of global Hopf bifurcation.
作者 魏章志 王良龙
机构地区 宿州学院数学与统计学院 安徽大学数学科学学院
出处 《大学数学》 2011年第1期80-84,共5页 College Mathematics
基金 安徽省自然科学基金项目(070416225) 安徽省教育厅高校优秀青年人才基金项目(2009SQRZ169) 宿州学院自然科学基金项目(2008yzk01)
关键词 时滞 稳定性 HOPF分支 delay stability Hopf bifurcation
分类号 O175.14 [理学—基础数学]
  • 相关文献

参考文献7

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二级参考文献14

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共引文献26

同被引文献44

  • 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马之恩,周义仓.常微分方程的定性与稳定性方法[M].北京:科学出版社,2001.
  • 3Cooke K,Grossman Z. Discrete delay,delay,distributed delay and stability switchs[J]. J Math Anal Appl,1982,86.592 - 27.
  • 4Wang Wendi,Ma Zhien. Harm less delay for uniform persistence[J]. J Math Anal Appl,1991,158(1):256 - 268.
  • 5Freedman H I, Strea Hari Rao V. The trade-off between mutual interference and time lags in predator-prey systems[J]. Bull Math Boil, 1983,45(6) : 991 - 1004.
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  • 7SONG Yongli, WEI Junjie. Local Hopf Bifurcation and Global Periodic Solutions in a Delayed Predator-Prey System [J]. Journal of Mathematical Analysis and Applications, 2005, 301(1): 1 -21.
  • 8WEN Xianzhang, WANG Zhicheng. The Existence of Periodic Solutions for Some Models with Delay [J]. Nonlinear Analysis Real World Applications, 2002, 3(4): 567 -581.
  • 9ZHANG Yongpo, MA Mingiuan, HUANG Qingdao. Analysis of Predator-Prey Model with Disease in the Prey [J]. Journal of Jilin University (Science Edition), 2011, 49(2): 191- 194.
  • 10SONG Zhiqiang, WAN Aying. Stability and Hopf Bifurcation Analysis in a Mutualistic System with Delays [J]. Journal of Chongqing Normal University (Natural Science), 2013, 30(3): 55-58.

引证文献8

二级引证文献9

大学数学
2011年 第1期

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