| 时标上具Allee效应的动力学方程的概周期解 |
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| 引用本文： | 王丽丽,胡猛.时标上具Allee效应的动力学方程的概周期解[J].数学杂志,2017,37(2):283-290. |
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| 作者姓名： | 王丽丽 胡猛 |
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| 作者单位： | 安阳师范学院数学与统计学院, 河南 安阳 455000,安阳师范学院数学与统计学院, 河南 安阳 455000 |
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| 基金项目： | Supported by Key Project of Scientific Research in Colleges and Universities in Henan Province (15A110004; 16A110008); Basic and Frontier Technology Research Project of Henan Province (142300410113). |
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| 摘 要： | 本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理，得到了方程存在唯一概周期解的充分条件.此外，通过构建适当的Laypunov函数，得到了概周期解是全局指数稳定的充分条件.
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| 关 键 词： | 动力学方程 Allee效应 概周期解 指数稳定 时标 |
| 收稿时间： | 2015/12/13 0:00:00 |
| 修稿时间： | 2016/3/4 0:00:00 |
ALMOST PERIODIC SOLUTION FOR A DYNAMICAL EQUATION WITH ALLEE EFFECTS ON TIME SCALES |
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| WANG Li-li and HU Meng.ALMOST PERIODIC SOLUTION FOR A DYNAMICAL EQUATION WITH ALLEE EFFECTS ON TIME SCALES[J].Journal of Mathematics,2017,37(2):283-290. |
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| Authors: | WANG Li-li and HU Meng |
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| Institution: | School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China and School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China |
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| Abstract: | This paper is concerned with an equation representing dynamics of a renewable resource subjected to Allee effects on time scales.By using exponential dichotomy of linear system and contraction mapping fixed point theorem,sufficient conditions are established for the existence of unique positive almost periodic solution.Moreover,by constructing a suitable Lyapunov functional,we obtain sufficient conditions for the global exponential stability of the almost periodic solution. |
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| Keywords: | dynamical equation Allee effect almost periodic solution global exponential stability time scale |
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