| 一类具有S型功能性反应系统的稳定性 |
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| 引用本文： | 梁娟,尹礼寿,刘岩岩.一类具有S型功能性反应系统的稳定性[J].重庆工商大学学报(自然科学版),2014(10):1-5. |
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| 作者姓名： | 梁娟 尹礼寿 刘岩岩 |
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| 作者单位： | 太原工业学院理学系;重庆大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(11171360);太原工业学院院基金(2011LQ01) |
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| 摘 要： | 考虑S型功能性反应模型的捕食-被捕食系统的动力性态,应用规范形理论和平面系统的定性理论研究了生物模型的定性性质,得到了平衡点在各种不同参数下的局部性质;在不同的参数下,它们可以为鞍点、稳定结点、鞍-结点、不稳定结点、弱中心等;利用计算第一系数的方法,研究了弱中心附近的超临界Hopf分岔,并在弱中心附近分支出唯一的极限环.
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| 关 键 词： | 平衡点 Hopf分支 极限环 弱中心 |
The Stability for a Class of Systems with S-type Functional Response |
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| LIANG Juan;YIN Li-shou;LIU Yan-yan.The Stability for a Class of Systems with S-type Functional Response[J].Journal of Chongqing Technology and Business University:Natural Science Edition,2014(10):1-5. |
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| Authors: | LIANG Juan;YIN Li-shou;LIU Yan-yan |
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| Institution: | LIANG Juan;YIN Li-shou;LIU Yan-yan;Department of Science Taiyuan Institute of Technology;School of Mathematics and Statistics,Chongqing University; |
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| Abstract: | This paper considers the dynamitic property of predator-prey system of S-type functional response model,uses normal form theory and qualitative theory of planner system to study the qualitative property of biological model,obtains local property of the balanced point under all kinds of parameters,indicates that under different parameters,they can be saddle point,stable node,saddle-node,unstable node,weak center and so on,uses the method to calculate the first coefficient to study the supercritical Hopf bifurcation near weak center and branches an only limit loop near the weak center. |
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| Keywords: | balanced point Hopf bifurcation limit loop weak center |
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