| 一类基于比率的捕食-食饵系统的全局稳定性分析 |
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| 引用本文： | 鲁铁军,王美娟,刘妍. 一类基于比率的捕食-食饵系统的全局稳定性分析[J]. 应用数学和力学, 2008, 29(4): 447-452. DOI: 10.3879/j.issn.1000-0887.2008.04.007 |
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| 作者姓名： | 鲁铁军 王美娟 刘妍 |
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| 作者单位： | 上海理工大学 理学院,上海 200093 |
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| 摘 要： | 研究一类基于比率和具第Ⅲ类功能性反应的捕食-食饵系统．通过分析正平衡点的局部稳定性给出了系统正平衡点全局渐近稳定以及系统存在极限环的条件．运用Hopf分支理论讨论了当正平衡点是非双曲型时的情形．
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| 关 键 词： | 比率 全局渐近稳定 功能性反应 Hopf分支 |
| 文章编号： | 1000-0887(2008)04-0447-06 |
| 收稿时间： | 2007-08-12 |
| 修稿时间： | 2007-08-12 |
Global Stability Analysis of a Ratio-Dependent Predator-Prey System |
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| LU Tie-jun,WANG Mei-juan,LIU Yan. Global Stability Analysis of a Ratio-Dependent Predator-Prey System[J]. Applied Mathematics and Mechanics, 2008, 29(4): 447-452. DOI: 10.3879/j.issn.1000-0887.2008.04.007 |
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| Authors: | LU Tie-jun WANG Mei-juan LIU Yan |
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| Affiliation: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China |
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| Abstract: | A ratio dependent predator-prey system with Holling type ó functional response was considered.The sufficient condition of the global asymptotic stability for the positive equilibrium and the existence of the limit cycle were given by studying the locally asymptotic stability of the positive equilibrium.At last,the condition when the positive equilibrium is no hyperbolic equilibrium was discussed by Hopf bifurcation. |
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