| 时滞捕食-食饵系统的局部Hopf分支和稳定性 |
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| 引用本文： | 马战平,冯立波.时滞捕食-食饵系统的局部Hopf分支和稳定性[J].大理学院学报,2009,8(8):1-6,11. |
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| 作者姓名： | 马战平 冯立波 |
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| 作者单位： | 大理学院数学与计算机学院,云南大理,671003 |
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| 基金项目： | 大理学院科研基金资助项目(2008X34) |
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| 摘 要： | 研究了食饵具有自时滞反馈的半比例依赖的捕食-食饵系统,证明了在一定条件下系统的持久性。通过分析正平衡点的特征方程,研究系统的线性稳定性和局部Hopf分支。通过构造适当的Lyapunov泛函,导出了系统正平衡点全局渐近稳定的充分条件。同时给出数值模拟的例子。
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| 关 键 词： | 时滞 持久性 Hopf分支 全局稳定性 |
Local Hopf Bifurcation and Stability of a Delayed Predator-Prey System |
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| Ma Zhanping,Feng Libo.Local Hopf Bifurcation and Stability of a Delayed Predator-Prey System[J].Journal of Dali University,2009,8(8):1-6,11. |
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| Authors: | Ma Zhanping Feng Libo |
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| Institution: | College of Mathematics and Computer Science;Dali University;Dali;Yunnan 671003;China |
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| Abstract: | A delayed semi ratio-dependent predator-prey system is investigated.It is proved that the system is permanent under in certain conditions.By analyzing the characteristic equation of positive equilibrium,the linear stability of the system is investigated and local Hopf bifurcation are demonstrated.Sufficient conditions for global asymptotic stability of the positive equilibrium are derived by constructing suitable Lyapunov functional.Finally,numerical simulations supporting our theoretical results are also i... |
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| Keywords: | time delay permanence Hopf bifurcation global stability |
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