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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Jingping Lu,
  • Jie Yao,
  • Qinlong Wang

摘要

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.