华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (6): 186-198.

• 应用数学与基础数学 • 上一篇    

一类含时滞与收获的捕食系统的Hopf分支分析

饶 凤1, 王玮明2, 李志斌1   

  1. 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
  • 收稿日期:2010-01-01 修回日期:2010-04-01 出版日期:2010-11-25 发布日期:2010-11-25
  • 通讯作者: 李志斌

Hopf bifurcation analysis of a predator-prey system with delay and harvesting

RAO Feng 1, WANG Wei-ming 2, LI Zhi-bin 1   

  1. 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
  • Received:2010-01-01 Revised:2010-04-01 Online:2010-11-25 Published:2010-11-25
  • Contact: LI Zhi-bin

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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.

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

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 bifurcation can occur as the delay τ 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.

Key words: time delay, Hopf bifurcation, stability, predator-prey system, time delay, Hopf bifurcation, stability

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