| 一类含时滞与收获的捕食系统的Hopf分支分析(英文) |
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| 引用本文： | 饶凤,王玮明,李志斌.一类含时滞与收获的捕食系统的Hopf分支分析(英文)[J].华东师范大学学报(自然科学版),2010,2010(6):186-198. |
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| 作者姓名： | 饶凤 王玮明 李志斌 |
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| 作者单位： | 1. 华东师范大学,计算机科学技术系,上海,200241
2. 温州大学,数学与信息科学学院,浙江温州,325035 |
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| 基金项目： | 国家自然科学基金，浙江省科学基金 |
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| 摘 要： | 运用定性分析和分支理论,研究了一类含时滞与收获的Monod-Haldane型捕食系统的动力学行为,确定了Hopf分支发生时的时滞τ的临界条件,并通过规范型理论和中心流行定理,研究了Hopf分支的方向与稳定性等.最后,利用数值模拟验证了研究结果.
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| 关 键 词： | 捕食系统 时滞 Hopf分支 稳定性 捕食系统 时滞 Hopf分支 稳定性 |
| 收稿时间： | 2010-1-1 |
| 修稿时间： | 2010-4-1 |
Hopf bifurcation analysis of a predator-prey system with delay and harvesting |
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| RAO Feng,WANG Wei-ming,LI Zhi-bin.Hopf bifurcation analysis of a predator-prey system with delay and harvesting[J].Journal of East China Normal University(Natural Science),2010,2010(6):186-198. |
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| Authors: | RAO Feng WANG Wei-ming LI Zhi-bin |
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| Institution: | 1. Department of Computer Science and Technology, East China Normal University, Shanghai 200241, China
2. College of Mathematics and Information Science, Wenzhou University, Wenzhou Zhejiang 325035, China |
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| Abstract: | In this paper, by using the analysis of qualitative method and bifurcation theory, we investigated the dynamics of the Monod-Haldane type predator-prey system with constant prey harvesting and a single time delay. It is shown that the Hopf bifurcati on can occur as the delay r crosses some critical values. Furthermore, the direction and stability of the Hopf bifurcation are determined by deriving normal form theory and center manifold theorem. Finally, numerical simulations are performed to illustrate the analytical results. |
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| Keywords: | predator-prey system time delay Hopf bifurcation stability |
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