| 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. |
| 关键词: Kolmogorov系统 极限环 闭轨 |
| DOI： |
| 投稿时间：2005-11-15修订日期：2006-03-16 |
| 基金项目:广西科学基金(0575092)资助 |
|
| The Limit Cycle of a Class of 2n-degree Kolmogorov's System |
|
ZHANG Li, HUANG Wen-tao
|
| (Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| 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. |
| Key words: Kolmogorov's system limit cycle closed orbit |
