| 带有第三边值的捕食模型的正稳态解的存在性 |
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| 引用本文： | 曾宪忠.带有第三边值的捕食模型的正稳态解的存在性[J].应用数学学报,2006,29(5):801-820. |
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| 作者姓名： | 曾宪忠 |
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| 作者单位： | 湖南师范大学数学与计算机学院,长沙,410081;湖南科技大学数学与计算科学学院,湘潭411201 |
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| 基金项目： | 国家自然科学基金;湖南省教育厅科研项目 |
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| 摘 要： | 本文研究了一个捕食者带有第三类边界条件、被捕食者带有Neumann边界条件的捕食模型．获得了捕食模型正稳态解的存在性和非存在性结果．并且,证明了它的正稳态解的局部稳定性和唯一性．
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| 关 键 词： | 捕食模型 正稳态解的存在性 度理论 分支理论 稳定性 唯—性 |
| 收稿时间： | 2004-09-07 |
| 修稿时间： | 2004-09-072006-07-26 |
Existence of Positive Stationary Solutions for A Prey-predator Model with The Third Boundary Condition to Predator |
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| ZENG XIANZHONG.Existence of Positive Stationary Solutions for A Prey-predator Model with The Third Boundary Condition to Predator[J].Acta Mathematicae Applicatae Sinica,2006,29(5):801-820. |
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| Authors: | ZENG XIANZHONG |
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| Institution: | 1.Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201;2.Department of Mathematics, Hunan Normal University, Changsha 410081 |
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| Abstract: | This paper deals with a prey-predator model in which the predator is with the homogeneous Robin boundary condition and the prey with the homogeneous Neumann boundary condition. We obtain some results of the existence and non-existence of its positive steady-state solutions. Furthermore, we demonstrate the local stability and uniqueness of its positive stationary solution. |
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| Keywords: | prey-predator model existence of positive steady-state solutions degree theory bifurcation theory stability uniqueness |
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