| 带保护区域的捕食-食饵模型平衡解的分歧与稳定性 |
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| 引用本文： | 郭改慧,李艳玲.带保护区域的捕食-食饵模型平衡解的分歧与稳定性[J].陕西师范大学学报,2007,35(2):27-30,124. |
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| 作者姓名： | 郭改慧 李艳玲 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 陕西西安710062 |
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| 摘 要： | 研究了一类带保护区域的捕食-食饵模型正平衡解的分歧及稳定性.利用特征值分歧理论和谱分析的方法,分别以b、m为分歧参数,证明了系统在半平凡解(a,0)及(0,b)附近出现分歧现象,得到了该模型正平衡解存在的充分条件.同时运用线性特征值的扰动理论和分歧解的稳定性理论给出了该分歧解的稳定性,即系统在(a,0)附近的分歧解是无条件稳定的;当I>0时,系统在(0,b)附近的分歧解是稳定的,而当I<0时,分歧解是不稳定的,其中I是一个积分.
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| 关 键 词： | 椭圆型微分方程 保护区域 分歧 稳定性 |
| 文章编号： | 1672-4291（2007）02-027-04 |
| 修稿时间： | 2007-01-15 |
The bifurcation and stability of the steady-state solutions for a predator-prey model with a protection zone |
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| GUO Gai-hui,LI Yan-ling.The bifurcation and stability of the steady-state solutions for a predator-prey model with a protection zone[J].Journal of Shaanxi Normal University: Nat Sci Ed,2007,35(2):27-30,124. |
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| Authors: | GUO Gai-hui LI Yan-ling |
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| Abstract: | The bifurcation and the stability of a predator-prey model with a protection zone are investigated by the methods of spectral analysis and bifurcation theory.The bifurcations from the semi-trivial solutions(a,0) and(0,b) are obtained by treating b and m as bifurcation parameters.Some sufficient conditions for the existence of positive solution are given.Moreover,some stability results of the bifurcation solutions are obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions. |
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| Keywords: | elliptic differential equation protection zone bifurcation stability |
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