| 被捕食者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： | 顾永耕,曾宪忠.被捕食者带有第三边值的捕食模型的正稳态解的存在性[J].数学物理学报(A辑),2007,27(2):248-262. |
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| 作者姓名： | 顾永耕 曾宪忠 |
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| 作者单位： | 湖南师范大学数学学院，湖南师范大学数学学院，湖南科技大学数学学院 湘潭 411201 长沙 410081，长沙 410081 |
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| 基金项目： | 国家自然科学基金;湖南省教育厅自然科学基金 |
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| 摘 要： | 该文研究了一类被捕食者带有第三边值的捕食模型. 首先获得了它存在正稳态解的充要条件是a>mb+d1λ1; 然后研究了它的正稳态解的局部稳定性和唯一性;最后讨论了充分大的扩散参数对它的正稳态解的存在性的影响.
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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 唯一性 |
| 文章编号： | 1003-3998(2007)02-248-15 |
| 收稿时间： | 2005-09-23 |
| 修稿时间： | 2005-09-23 |
Existence of Positive Stationary Solutions for a Prey-predator Model with the Third Boundary Value to the Prey |
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| Gu Yonggeng,Zeng Xianzhong.Existence of Positive Stationary Solutions for a Prey-predator Model with the Third Boundary Value to the Prey[J].Acta Mathematica Scientia,2007,27(2):248-262. |
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| Authors: | Gu Yonggeng Zeng Xianzhong |
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| Affiliation: | 1. Department of Mathematics, Hunan Normal University, Changsha 410081; 2.Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201 |
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| Abstract: | This paper deals with a prey-predator model with the third boundary value to the prey. First, the authors obtain that the model has positive stationary solutions if and only if a>mb+d1λ1. Secondly, the authors prove the localstability and uniqueness of its positive stationary solution. Thirdly, the authors study the change of existence of its positive stationary solution when the coefficients of its diffusion terms approach infinity. |
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| Keywords: | Prey-predator model Existence of positive stationary solutions Degree theory Bifurcation theory Stability Uniqueness |
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