| 一类比率型功能性反应捕食模型的稳定性分析 |
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| 引用本文： | 张剑,张宏民,堵秀凤. 一类比率型功能性反应捕食模型的稳定性分析[J]. 数学的实践与认识, 2011, 41(10) |
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| 作者姓名： | 张剑 张宏民 堵秀凤 |
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| 作者单位： | 齐齐哈尔大学理学院,齐齐哈尔,161006 |
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| 基金项目： | 黑龙江省自然科学基金，齐齐哈尔大学青年教师科研启动支持计划-科学技术类一般项目 |
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| 摘 要： | 研究了一类具有比率型功能性反应的捕食模型,对模型进行了定性和稳定性分析,讨论了模型唯一正平衡点的存在条件,以及模型各个平衡点的性态.得到了各个平衡点全局渐近稳定的充分条件.通过绘制模型的相轨线,分析轨线的走向得到了原点全局渐近稳定的条件,并证明了模型不存在非平凡正周期解的条件,通过构造Lyapunov函数得到了模型的唯一正平衡点是全局渐近稳定的结论.
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| 关 键 词： | 比率型功能性反应 平衡点 全局渐近稳定 Lyapunov函数 |
Stability Analysis of a Ratio-Dependent Functional Response Predator-Prey Model |
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| ZHANG Jian,ZHANG Hong-min,DU Xiu-feng. Stability Analysis of a Ratio-Dependent Functional Response Predator-Prey Model[J]. Mathematics in Practice and Theory, 2011, 41(10) |
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| Authors: | ZHANG Jian ZHANG Hong-min DU Xiu-feng |
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| Affiliation: | ZHANG Jian,ZHANG Hong-min,DU Xiu-feng (College of Science,Qiqihar University,Qiqihar 161006,China) |
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| Abstract: | In this paper,a ratio-dependent functional response predator-prey model is researched, the model of qualitative and stable analysis are discussed.The existential condition of unique positive equilibrium and properties of every equilibrium are also discussed.Particularly, the sufficient conditions of globally asymptotic stability of every equilibrium are obtained.By drawing the path curve and analyzing the directions of the curve,the paper gets the condition of globally asymptotic stability of origin.And it ... |
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| Keywords: | ratio-dependent functional response equilibrium globally asymptotic stability Lyapunov function |
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