| 水生生态系统中有竞争和捕食效应的一类简单食物网模型的稳定性分析 |
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| 引用本文： | 梁英琼,刘贤宁,吕万碧. 水生生态系统中有竞争和捕食效应的一类简单食物网模型的稳定性分析[J]. 西南大学学报, 2010, 32(3) |
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| 作者姓名： | 梁英琼 刘贤宁 吕万碧 |
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| 作者单位： | 西南大学数学与统计学院,重庆,400715 |
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| 基金项目： | 教育科学技术研究重点项目，教育部留学回国人员科研启动基金 |
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| 摘 要： | 提出了水生生态系统中有竞争和捕食的一类简单食物网模型.首先讨论了平衡点的存在条件,利用Hurwitz判据分析了局部渐近稳定性;通过构造Lyapunov函数得到了系统全局渐近稳定的条件,并具体解释了其生物含义.从以上讨论中得到了控制3类物种存活、灭绝或共存的4个阈值.生物分析表明,水草和鱼在控制富营养化问题中起着极其重要的作用.Abstract：In this paper, a simple food web model with competition and predation in aquatic ecosystems is proposed.The existence conditions of equilibria are discussed and the local asymptotic stability is analyzed.By means of Lya-punov functions, the global asymptotic stability of the model is obtained.Four thresholds, which indicate the coex-istence, survival or extinction of 3 species, are obtained from the above discussions.Bio-analysis shows that aquatic weeds and fish play an important role in the control of eutrophication.
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| 关 键 词： | 稳定性 Hurwitz判据 Lyapunov函数 水生生态系统 |
Stability Analysis of a Simple Food Web Model with Competition and Predation in Aquatic Ecosystems |
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| LIANG Ying-qiong,LIU Xian-ning,L Wan-bi. Stability Analysis of a Simple Food Web Model with Competition and Predation in Aquatic Ecosystems[J]. Journal of Southwest Agricultural University, 2010, 32(3) |
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| Authors: | LIANG Ying-qiong LIU Xian-ning L Wan-bi |
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| Affiliation: | LIANG Ying-qiong,LIU Xian-ning,L(U) Wan-bi |
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