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时滞Nicholson's Blowflies方程中行波解的Hopf分支 被引量：3

Hopf Bifurcation of Traveling Wave of Delayed Nicholson's Blowflies Equation
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摘要 主要利用时滞微分方程中Hopf分支理论探讨时滞Nicholson's Blowflies方程中行波解随时滞量τ大小变化的分支行为.结果发现时滞量经过某一数值τ_0=1/(cω_0) arcsin-cω_0/p时,原系统会产生分支现象,最终导致形成周期性行波解. Mainly employing Hopf bifurcation theory of delayed differential equation to study the bifurcation behavior of the traveling wave solution of the delayed Nicholson＇s Blowflies equation as the delayed termτchanges.The results showed that when the delayed termτpass throughτ_0=1/（cω_0）arcsin（-cω_0）/p,the original system will take place bifurcation phenomenon and eventually lead to become the periodic traveling wave solution.
作者 杨高翔 赵临龙
机构地区 安康学院数学系
出处 《生物数学学报》 CSCD 北大核心 2011年第1期81-86,共6页 Journal of Biomathematics
基金 安康学院(2008AKXY025) (AYQDZR200906)
关键词 时滞Nicholson's Blowflies方程 行波解 HOPF分支 Delayed Nicholson＇s Blowflies equation Traveling wave solution Hopf bifurcation
分类号 O193 [理学—基础数学] O175.29 [理学—基础数学]
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参考文献7

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同被引文献28

  • 1谭欣欣,冯恩民,沈伯骞.双曲线边界二次系统单中心环域的Poincaré分支[J].大连理工大学学报,2005,45(2):298-302. 被引量：3
  • 2邵仪,赵育林.一类双中心平面二次系统的Abel积分零点个数[J].数学学报（中文版）,2007,50(2):451-460. 被引量：5
  • 3Hassard B,Kazarinoff D,Wan Y.Theory and Applications of Hopf Bifurcation[M].Cambridge:Cambridge University Press,1981.
  • 4Ruan S,Wei J.On the zeros of transcendental functions with applications to stability of delay differential equations with two delays[J].Dynamic Analysis of Spatial Structures Session Organizer,2003,10(6):863- 874.
  • 5Song Y,Peng Y.Stability and bifurcation analysis on a Logistic model with discrete and distributed delays[J]. Applied Mathematics and Computation,2006,181(2):1745-1757.
  • 6May R M.Time delay versus stability in population models with two and three trophic levels[J].Ecology, 1973,4(2):315-325.
  • 7Yan X-P,Zhang C-H.Hopf bifurcation in a delayed Lokta-Volterra predator+prey system[J].Nonlinear Analysis:Real World Applications,2008,9(1):114-127.
  • 8Ma Z,Huo H.Stability and Hopf bifurcation analysis on a predator-prey model with discrete and distributed delays[J].Nonlinear Analysis:Real World Applications,2009,10(2):1160-1172.
  • 9Chen Y,Song C.Stability and Hopf bifurcation analysis in a prey-predator system with stage-structure for prey and time delay[J].Chaos Solitons Fractals,2008,8(1):1104-1114.
  • 10Meng X,Wei J.Stability and bifurcation of mutual system with time delay[J].Chaos,Solitons and Fractals, 2004,21(3):729-40.

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生物数学学报
2011年 第1期

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