Center and Degenerate Hopf Bifurcation Cyclicity of high-order Singularity in a Class of Three-Dimensional Systems

• Jingping Lu ^[1] ; Jie Yao ^[1] ; Qinlong Wang ^[1]
  1. [1] Guilin University of Electronic Technology

     Guilin University of Electronic Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This study investigates the degenerate Hopf bifurcation occurring at a high-order degenerate singular point in a class of three-dimensional systems. Using the center manifold theorem, we propose a novel complex symmetric formal series method that allows direct computation of singular point quantities without reducing the original three-dimensional system to a two-dimensional form. Additionally, two specific classes of differential systems are analyzed, leading to a complete resolution of the center problem and the determination of the cyclicity of degenerate Hopf bifurcation for high-order singularities. This work offers new insights into the Hopf bifurcation associated with degenerate singular points.

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