Journal of Guangxi Normal University(Natural Science Edition) ›› 2026, Vol. 44 ›› Issue (1): 102-109.doi: 10.16088/j.issn.1001-6600.2025012401

• Mathematics and Statistics • Previous Articles     Next Articles

Cyclicity of High-order Singular Point Degenerate Hopf Bifurcation for a Class of Three-dimensional Systems

YAO Jie, WANG Qinlong*   

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China
  • Received:2025-01-24 Revised:2025-03-14 Online:2026-01-05 Published:2026-01-26

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Abstract: In this paper, the degenerate Hopf bifurcation is investigated at high-order singular point in a class of three-dimensional systems. Based on the center manifold theorem, a formal series method for directly calculating singularity quantities is proposed, which avoids the tedious process of converting the original three-dimensional system into the plane reduction equations. The corresponding linear recursive formula of this algorithm is easy to execute. A class of fourth-order system is specifically studied, its center problem of high-order singular points is solved and the cyclicity of degenerate Hopf bifurcation is determined.

Key words: higher-order singularity, degenerate Hopf cyclicity, center problem, singular point quantities

CLC Number:  O175.1
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