| 具有反馈控制单种群模型周期解的存在性与唯一性 |
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| 引用本文： | 田德生,喻枫.具有反馈控制单种群模型周期解的存在性与唯一性[J].湖北工业大学学报,2007,22(5):92-96. |
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| 作者姓名： | 田德生 喻枫 |
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| 作者单位： | 湖北工业大学理学院,湖北,武汉,430068;襄樊职业技术学院,湖北,襄樊,441050 |
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| 摘 要： | 考虑具有反馈控制的单种群周期系数模型,这是一个二维系统.通过将其转化为一维系统,应用重合度定理的方法,证明了该系统至少存在一个正的周期解,进而证明了此周期解是全局渐近稳定的,是唯一的.将常系数模型作比较,得到了常系数模型系统平衡点的全局渐近稳定性的结论.
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| 关 键 词： | 单种群模型 周期解 平衡点 全局渐近稳定性 |
| 文章编号： | 1003-4684（2007）05-0092-05 |
| 收稿时间： | 2007-06-30 |
| 修稿时间： | 2007年6月30日 |
Existence and Uniqueness of Periodic Solution for a Single-Species Model with Feedback Control |
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| TIAN De-sheng,YU Feng.Existence and Uniqueness of Periodic Solution for a Single-Species Model with Feedback Control[J].Journal of Hubei University of Technology,2007,22(5):92-96. |
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| Authors: | TIAN De-sheng YU Feng |
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| Abstract: | In this paper,a single-species model with feedback control which is of periodic coefficients is studied.The model is a two-dimensional system.By converting such a system into one-dimensional one,the existence of at least one positive periodic solution of this system is proved by means of the method of coincidence degree.Moreover,it is shown that the periodic solution is globally asymptotically stable and unique.Compared with the system of constant coefficients,the equilibrium of the system of constant coefficients is globally asymptotically stable. |
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| Keywords: | single-species model periodic solution equilibrium global asymptotical stability |
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