| 一类2n次Kolmogorov系统的极限环 |
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| 引用本文： | 张理,黄文韬. 一类2n次Kolmogorov系统的极限环[J]. 广西科学, 2006, 13(3): 180-183 |
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| 作者姓名： | 张理 黄文韬 |
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| 作者单位： | 桂林电子工业学院计算科学与数学系,广西桂林,541004 |
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| 摘 要： | 研究一类2n次Kolmogorov系统{dx/dt=x(a0-a1x a3x3-a4x4 a5xy2n-1),dy/dt=y(b1x2n-b2),极限环的存在性问题.主要讨论a5＞0和a5＜0两种情形.当a5＞0时,系统在第一象限内不存在极限环;当a5＜0时,得到了平衡点的稳定性态,系统无闭轨的充分条件以及在第一象限内存在稳定极限环的条件.
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| 关 键 词： | Kolmogorov系统 极限环 闭轨 |
| 文章编号： | 1005-9164（2006）03-0180-04 |
| 收稿时间： | 2005-11-15 |
| 修稿时间： | 2006-03-16 |
The Limit Cycle of a Class of 2n-degree Kolmogorov''s System |
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| ZHANG Li and HUANG Wen-tao. The Limit Cycle of a Class of 2n-degree Kolmogorov''s System[J]. Guangxi Sciences, 2006, 13(3): 180-183 |
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| Authors: | ZHANG Li and HUANG Wen-tao |
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| Affiliation: | Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China |
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| Abstract: | The problem about the existence of a limit cycle of a class of 2n-degree Kolmogorov''s system dx/dt=x (a0-a1x+a3x3-a4x4+a5xy2n-1), dy/dt=y (b1x2n-b2), is studied, and the system is discussed mainly when a5>0 and a5<0, respectively.A system has not limit cycles in the first quadrant when a5>0.The stability of equilibrium, the sufficient conditions of nonexistence of closed orbits and the conditions of existence of a stable limit cycles of the system in the first quadrant are obtained when a5<0. |
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| Keywords: | Kolmogorov''s system limit cycle closed orbit |
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