| 一类具有时滞的捕食者-食饵系统的数值逼近 |
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| 引用本文： | 王玲书,冯光辉.一类具有时滞的捕食者-食饵系统的数值逼近[J].吉林林学院学报,2010(3):193-196. |
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| 作者姓名： | 王玲书 冯光辉 |
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| 作者单位： | [1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]军械工程学院基础部,河北石家庄050003 |
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| 基金项目： | 河北省教育厅科学研究计划项目（2009114） |
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| 摘 要： | 研究了一类具有时滞的捕食系统的数值逼近问题.运用离散动力系统的分支理论,在该系统具有Hopf分支的条件下,讨论了欧拉方法数值求解该系统时,差分方程Hopf分支的存在性以及连续系统与其数值逼近间的关系.证明了当该系统在τ=0τ处产生Hopf分支且时间步长充分小时,其数值解在相应的参数值τh处也存在Hopf分支.
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| 关 键 词： | 捕食系统 时滞 Hopf分支 数值逼近 |
Numerical Approximation for a Predator-Prey System with Time Delay |
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| Authors: | WANG Ling-shu FENG Guang-hui |
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| Affiliation: | 1.School of Mathematics and Statistics,Hebei University of Economics ＆ Business,Shijiazhuang 050061,China;2.Basic Department of Mechanical Engineering College,Shijiazhuang 050003,China) |
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| Abstract: | The numerical approximation of a predator-prey system with time delay is investigated.Hopf bifurcations are established by choosing time delay as the parameter.The Hopf bifurcation of deference equation obtained by using Euler method is considered.The relations of Hopf bifurcation between the continuous system and its numerical approximation are discussed.It proves that the numerical solutions can preserve the Hopf bifurcation when time step small enough. |
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| Keywords: | predator-prey system time delay Hopf bifurcation numerical approximation |
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