| 具有无限时滞离散的Predator-Prey系统周期正解的存在性 |
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| 引用本文： | 蒋利群,莫宏敏. 具有无限时滞离散的Predator-Prey系统周期正解的存在性[J]. 吉首大学学报(自然科学版), 2003, 24(2): 52-56 |
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| 作者姓名： | 蒋利群 莫宏敏 |
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| 作者单位： | (1.吉首大学数学与计算机科学系，湖南 吉首 416000；2.湖南大学数学与计量经济学院，湖南 长沙 410082) |
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| 摘 要： | 研究了具有三个物种周期的Predator-Prey差分模型，用拓扑度理论讨论了具有无限时滞差分系统的周期正解的存在性，证明了具有无限时滞差分系统的正周期解存在的充分条件为：(ⅰ)r-1a-32-r-3a-12ｅｘｐ（2r-2ω）＞0；（ⅱ）r-1a-32-r-3a-12ｅｘｐ（2r-2ω）-r-2a-11a-32ｅｘｐ（2r-1ω）＜0；（ⅲ）-a-32a-12r-1＋a-32a-11r-2＋a-21a-12r-3＜0．
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| 关 键 词： | Predator-Prey系统 正周期解 无限时滞 离散的 拓扑度 |
| 文章编号： | 1007-2985(2003)02-0052-05 |
| 修稿时间： | 2002-05-10 |
Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays |
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| JIANG Li-Qun,MO Hong-Min. Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays[J]. Journal of Jishou University(Natural Science Edition), 2003, 24(2): 52-56 |
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| Authors: | JIANG Li-Qun MO Hong-Min |
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| Affiliation: | (1.Dept.of Math.And Computer Science,Jishou University,Jishou 416000,Hunan China;2.College of Math.and Econometrics,Hunan University,Changsha 410082,Hunan China) |
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| Abstract: | The differential model of periodic Predator-Prey with three species is studied.The existence of positive periodic solution of this system with infinite delays is discussed by using the topologic theory.It is proved that the ample conditions for the existence of positive periodic solution of this system are as follows:(ⅰ)r-1a-32-r-3a-12ｅｘｐ（2r-2ω）＞0；（ⅱ）r-1a-32-r-3a-12ｅｘｐ（2r-2ω）-r-2a-11a-32ｅｘｐ（2r-1ω）＜0；（ⅲ）-a-32a-12r-1＋a-32a-11r-2＋a-21a-12r-3＜0． |
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| Keywords: | Predator-Prey system positive periodic solution infinite delays discrete topologic degree |
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