| 一类具有时滞的捕食——食饵系统的稳定性与Hopf分支 |
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| 引用本文： | 杨建雅,张凤琴.一类具有时滞的捕食——食饵系统的稳定性与Hopf分支[J].数学的实践与认识,2010,40(18). |
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| 作者姓名： | 杨建雅 张凤琴 |
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| 基金项目： | 山西省重点扶持学科，山西省自然科学基金 |
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| 摘 要： | 研究了一类具有时滞的捕食—食饵系统,通过分析正平衡点处的特征方程,讨论了系统正平衡点的稳定性;以时滞作为分支参数,应用Hopf分支理论,得到了系统存在Hopf分支的充分条件.
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| 关 键 词： | 捕食—食饵系统 平衡点 时滞 Hopf分支 |
Hopf Bifurcation of a Predator-Prey System with Time Delay |
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| YANG Jian-ya,ZHANG Feng-qin.Hopf Bifurcation of a Predator-Prey System with Time Delay[J].Mathematics in Practice and Theory,2010,40(18). |
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| Authors: | YANG Jian-ya ZHANG Feng-qin |
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| Abstract: | A predator-prey system with time delay is considered.By analyzing the characteristic equation of the linearized system of original system at the positive equilibrium,the stability of the positive equilibrium is discussed.By regarding the time delay as the bifurcation parameters and by applying the theorem of Hopf bifurcation,the sufficient conditions of the positive equilibrium occurring Hopf bifurcations are given. |
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| Keywords: | predator-prey system equilibrium time delay Hopf bifurcation |
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