| 一类五次多项式系统中心焦点的判定 |
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| 引用本文： | 唐 桥,刘兴国.一类五次多项式系统中心焦点的判定[J].湖南工业大学学报,2008,22(5):7-9. |
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| 作者姓名： | 唐 桥 刘兴国 |
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| 作者单位： | 湖南工业大学,理学院,湖南,株洲,412008 |
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| 摘 要： | 采用常微分方程定性理论的经典方法,对一类平面五次多项式系统进行定性分析。运用基于H.Poincaré思想的形式级数法,对系统进行细焦点的分析;利用对称原理对系统进行中心判定;利用Hopf分支理论根据参数变化时焦点稳定性的变化,分析得到极限环存在的若干充分条件。
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| 关 键 词： | 五次系统 中心 焦点 极限环 存在性 |
| 收稿时间： | 2008/6/24 0:00:00 |
Judging on Center-or-Focus for a Class of Quintic Polynomial System |
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| Tang Qiao and iu Xingguo.Judging on Center-or-Focus for a Class of Quintic Polynomial System[J].Journal of Hnnnan University of Technology,2008,22(5):7-9. |
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| Authors: | Tang Qiao and iu Xingguo |
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| Abstract: | By using qualitative classical theory of ordinary differential equation, a class of planar quintic polynomial differential system is qualitatively analyzed. The fine focus is analyzed by formal series method from the thoughts of H. Poincaré and the center is judged by using principle of symmetry. Then some sufficient conditions for the existence of limit cycles of such systems are also obtained after Hopf bifurcation theory. |
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| Keywords: | quintic system center focus limit cycle existence |
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