| 一类具时滞的Gompertz捕食模型的稳定性分析 |
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| 引用本文： | 李云飞,徐瑞,毛书学.一类具时滞的Gompertz捕食模型的稳定性分析[J].吉林林学院学报,2011(1):18-22. |
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| 作者姓名： | 李云飞 徐瑞 毛书学 |
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| 作者单位： | 军械工程学院应用数学研究所,河北石家庄050003 |
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| 基金项目： | 国家自然科学基金项目（10671209 11071254） |
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| 摘 要： | 研究一类具有时滞的Gompertz增长率的捕食-被捕食模型,通过分析特征方程讨论了正平衡点的局部稳定性;通过构造适当的Lyapunov泛函,得到了保证系统正平衡点全局渐近稳定的充分条件,并讨论了在正平衡点附近Hopf分支的存在性问题.当τ=0时,应用微分方程定性理论,得到了系统存在极限环的充分条件.
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| 关 键 词： | 时滞 Hopf分支 极限环 Lyapunov泛函 稳定性 |
Stability Analysis of a Gompertz Predator-prey Model with Time Delay |
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| Authors: | LI Yun-fei XU Rui MAO Shu-xue |
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| Institution: | (Institute of Applied Mathematics,Ordnance Engineering College,Shijiazhuang 050003,China) |
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| Abstract: | A predator-prey model with time delay and Gompertz growth rate is investigated.The local stability of a positive equilibrium is discussed by analyzing the corresponding characteristic equation.By constructing a suitable Lyapunov functional,the sufficient conditions are derived for the global asymptotic stability of the positive equilibrium.The existence of Hopf bifurcation is also addressed.When the time delay equals to 0,by using the qualitative theory of ordinary differential equations,the sufficient condition is obtained for the existence of limit cycle. |
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| Keywords: | time delay Hopf bifurcation limit cycle Lyapunov functional stability |
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