广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (5): 104-126.doi: 10.16088/j.issn.1001-6600.2022020702

• 综述 • 上一篇    下一篇

三维微分系统的极限环与等时中心

黄文韬1*, 古结平2, 王勤龙3   

  1. 1.广西师范大学 数学与统计学院, 广西 桂林 541006;
    2.广西职业师范学院 教育学院, 广西 南宁 530007;
    3.桂林电子科技大学 数学与计算科学学院, 广西 桂林 541004
  • 收稿日期:2022-02-07 修回日期:2022-04-12 出版日期:2022-09-25 发布日期:2022-10-18
  • 通讯作者: 黄文韬(1966—), 男, 广西永福人, 广西师范大学教授, 博导。E-mail: huangwentao@163.com
  • 基金资助:
    国家自然科学基金(12061016, 12161023); 广西科技计划项目(2021AC06001); 广西高校中青年教师科研基础能力提升项目(2022KY0904)

Limit Cycles and Isochronous Centers of Three-dimensional Differential Systems

HUANG Wentao1*, GU Jieping2, WANG Qinlong3   

  1. 1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China;
    2. School of Education, Guangxi Vocational Normal University, Nanning Guangxi 530007, China;
    3. School of Mathematics and Computational Science,Guilin University of Electronic Technology, Guilin Guangxi 541004, China
  • Received:2022-02-07 Revised:2022-04-12 Online:2022-09-25 Published:2022-10-18

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摘要： 微分动力系统的极限环与等时中心是微分方程定性理论中2个经典问题,也是微分方程定性理论领域的研究热点,其研究有重要理论意义和应用价值。相较于平面系统,三维微分系统的极限环与等时中心研究也是一项有挑战性的工作,系统复杂度与定性分析难度都有很大提升。本文主要介绍近几十年来三维微分系统的极限环与等时中心的研究进展,并给出该领域一些待解决的问题。

关键词: 三维微分系统, 极限环, 等时中心, 中心流形, Hopf分支

Abstract: Bifurcation of limit cycle and isochronous center of differential systems are classical problems in the qualitative theory of differential equations which are always hot topic in the research of differential equations. The study has important theoretical and applied value. Compared with planar systems, the research of limit cycle and isochronous center for three-dimensional differential systems is a more challenging work, and the complexity of the system and the difficulty of qualitative analysis have greatly been improved. This paper mainly introduces the research progress of limit cycles and isochronous centers of three-dimensional differential systems in recent decades, and puts forward some problems to be solved in this field.

Key words: three-dimensional differential system, limit cycle, isochronous center, center manifold, Hopf bifurcation

中图分类号: 

  • O175
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