| 一类多偏差变元的n种群Lotka-Volterra模型的周期正解 |
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| 引用本文： | 鲁世平,葛渭高.一类多偏差变元的n种群Lotka-Volterra模型的周期正解[J].数学学报,2005,48(3):427-438. |
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| 作者姓名： | 鲁世平 葛渭高 |
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| 作者单位： | [1]安徽师范大学数学系，芜湖241000 [2]北京理工大学数学系，北京100081 |
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| 基金项目： | 国家自然科学基金资助项目(1987100510371006)
安徽师范大学专项基金项目(2002ZXZ001) |
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| 摘 要： | 本文研究了一类多偏差变元Lotka-Volterra种群模型的间期正解问题,利用重合度拓展定理和一些分析技巧,得到了周期正解存在性的新结果.与已有文献相比,本文所讨论的模型更具一般性,它包含了以前人们所研究的竞争-种群模型、捕食-种群模型等,而且估计先验界的方法也是全新的.
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| 关 键 词： | 周期正解 重合度拓展定理 Lotka-Volterra种群模型 |
On the Existence of Positive Periodic Solutions for n-Species Lotka-Volterra Population Model with Multiple Deviating Arguments |
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| Shi Ping LU.On the Existence of Positive Periodic Solutions for n-Species Lotka-Volterra Population Model with Multiple Deviating Arguments[J].Acta Mathematica Sinica,2005,48(3):427-438. |
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| Authors: | Shi Ping LU |
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| Institution: | Shi Ping LU Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China Wei Gao GE Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | In this paper, using some analysis techniques and the continuation theorem of coincidence degree theory, the authors study a kind of n-species Lotka-Volterra population model with multiple deviating arguments. Some new results on the existence of positive periodic solutions are obtained. For the comparision, the model subject to this paper is more general, which includes some known Lotka-Volterra type systems, such as competitive systems, predator-prey systems and so on. Meanwhile, the method to estimate a priori bounds of periodic solutions is different from the corresponding ones found in the existing literature. |
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| Keywords: | Positive periodic Solution Continuation theorem of coincidence degree principle Lotka-Volterra population model |
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