| 具有扩散的捕食与被捕食系统的持续性和稳定性 |
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| 引用本文： | 桂占吉,葛渭高.具有扩散的捕食与被捕食系统的持续性和稳定性[J].系统科学与数学,2005,25(1):050-062. |
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| 作者姓名： | 桂占吉 葛渭高 |
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| 作者单位： | 1. 北京理工大学数学系,北京,100081;海南师范学院数学系,海口,571158
2. 北京理工大学数学系,北京,100081 |
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| 基金项目： | 国家自然科学基金(10371006)
海南省自然科学基金(80201)资助课题 |
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| 摘 要： | 本文研究了一类具有扩散和时滞的捕食与被捕食系统,证明了在适当条件下系统 是一致持续的,利用同伦技术证明了正平衡点的存在性,构造适当的Lyapunov函数获得 了正平衡点的局部和全局稳定的充分条件.
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| 关 键 词： | 捕食与被捕食系统 扩散 时滞 持续性 稳定性 |
| 修稿时间： | 2001年12月4日 |
PERMANENCE AND STABILITY FOR PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY |
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| Gui Zhanji,Ge Weigao.PERMANENCE AND STABILITY FOR PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY[J].Journal of Systems Science and Mathematical Sciences,2005,25(1):050-062. |
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| Authors: | Gui Zhanji Ge Weigao |
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| Institution: | (1)Department of Mathematics, Beijing Institute of Technology;Department of Mathematics, Hainan Normal University;(2)Department of Mathematics, Beijing Institute of Technology |
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| Abstract: | In this paper a Predator-Prey system with diffusion and time delay is established. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions for both local and global stability of the positive equilibrium are obtained by constructing a suitable Lyapunov function. |
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| Keywords: | Predator-Prey system diffusion time delay periodic solution delay stability |
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