Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (5): 104-126.doi: 10.16088/j.issn.1001-6600.2022020702

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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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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

CLC Number: 

  • O175
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