| 一类食饵-捕食系统的定性分析 |
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| 引用本文： | 罗廷友,刘启宽,李映辉.一类食饵-捕食系统的定性分析[J].四川理工学院学报(自然科学版),2011,24(2):154-158. |
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| 作者姓名： | 罗廷友 刘启宽 李映辉 |
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| 作者单位： | 1. 成都信息工程学院数学学院,成都,610225
2. 西南交通大学力学与工程学院,成都,610031 |
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| 基金项目： | 国家自然科学基金(11072204); 四川省应用基础研究计划(2010JY0079); 成都信息工程学院自然科学发展基金(CSRF200601) |
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| 摘 要： | 文章研究一类食饵具常数投放且增长率含h(x)的食饵-捕食系统。利用常微分方程定性和稳定性理论分析了平衡点的性态,借助Dulac函数法得到了正平衡点全局渐近稳定的充分条件,最后利用Poincare-Bendixson环域定理和张芷芬唯一性定理,证明了极限环存在唯一的充分条件,并给出了数值模拟结果。
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| 关 键 词： | 食饵-捕食系统 平衡点 增长率 极限环 |
Qualitative Analysis of a Kind of Predator-Prey System |
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| LUO Ting-you,LIU Qi-kuan,LI Ying-hui.Qualitative Analysis of a Kind of Predator-Prey System[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2011,24(2):154-158. |
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| Authors: | LUO Ting-you LIU Qi-kuan LI Ying-hui |
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| Institution: | LUO Ting-you1,LIU Qi-kuan1,LI Ying-hui2(1.College of Mathematics,Chengdu University of Information Technology,Chengdu 610225,China,2.School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China) |
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| Abstract: | In this paper,we study a qualitative analysis of predator-prey system with constant rate stocking and rate function which contains h(x).By using qualitative theory and stability theory in ordinary differential equation,we analyze the qualitative behavior of equilibrium points.And we find out the sufficient condition of global asymptotic stability of positive equilibrium points.Then,by using Poincare-Bendixson annular region theorem and uniqueness theorem by Zhang Zhi-fen,we prove the sufficient condition of... |
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| Keywords: | predator-prey system equilibrium points growth rate limit cycle |
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