| 一类具有时滞的生态系统的稳定性与分支分析 |
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| 引用本文： | 刘三红.一类具有时滞的生态系统的稳定性与分支分析[J].内蒙古师范大学学报(自然科学版),2007,36(5):549-550,554. |
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| 作者姓名： | 刘三红 |
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| 作者单位： | 咸宁学院数学系,湖北咸宁437005 |
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| 基金项目： | 湖北省教育厅自然科学基金;咸宁学院校内重点基金 |
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| 摘 要： | 研究了具有有限时滞的Lotka-Volterra捕食方程的解的性态，以时滞τ为参数，利用解析方法分析了方程平衡点的稳定性，得到在平衡点处产生稳定性和Hopf分支的充分条件及平衡点稳定性的存在范围．所得结果是对已有结论的改进和推广。
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| 关 键 词： | Lotka-Volterra系统 Hopf分支 渐近稳定 |
| 文章编号： | 1001-8735（2007）05-0549-02 |
| 收稿时间： | 2006-10-24 |
| 修稿时间： | 2006-10-24 |
Stability and Hopf Bifurcation in a Class of Ecological System with Time Delay |
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| LIU San-hong.Stability and Hopf Bifurcation in a Class of Ecological System with Time Delay[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2007,36(5):549-550,554. |
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| Authors: | LIU San-hong |
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| Institution: | Department of Mathematics, Xianning College, Xianning 437005, Hubei, China |
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| Abstract: | The properties of the solution in Predator-prey system with finite delay was studied. In much detail, using time lag r as a parameter and using analytical method, the stability and Hopf bifurcation of the equilibriums in Predator-prey system was analysed. The results we obtained are the sufficient condition of stability and the sufficient condition of the occurrence of Hopf bifurcation in equilibrium. We also obtain the limit of the stability of the equilibrium. The outcome of this paper is one that shown great improvement to the outcome which is in existence. |
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| Keywords: | Lotka-Volterra system Hopf bifurcation asymptotically stability |
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