摘要
对一类原点为三次幂零奇点的七次微分系统,利用已经计算出的该七次微分系统原点的前10个拟Lyapunov常数,经过分析推导,从而得出原点成为10阶细焦点的充要条件,在此条件的基础上对系统作微小扰动,进而得出在原点充分小的邻域内恰有10个包围原点的极限环的结论。
For a kind of the seven-order differential system, whose origin is the three-order nilpotent singular point, this paper makes use of the first ten quasi-Lyapunov constants from the calculated to probe into the sufficient conditions by which the origin becomes the fine focus of the ten-order. Based on the sufficient conditions, when the system is slightly perturbed, ten limit cycles are derived, which are in the neighborhood of the origin.
出处
《巢湖学院学报》
2014年第3期16-20,共5页
Journal of Chaohu University
基金
安徽省高等学校省级优秀青年人才基金项目(项目编号:2012SQRL150)
安徽省高校省级自然科学研究项目(项目编号:KJ2012B118)
关键词
幂零奇点
七次系统
细焦点
拟Lyapunov常数
极限环分支
three-order nilpotent singular point
the seven-order system
fine focus
quasi-Lyapunov constant
limit cycle bifurcation