Resumen de Center and Degenerate Hopf Bifurcation Cyclicity of high-order Singularity in a Class of Three-Dimensional Systems
Jingping Lu, Jie Yao, Qinlong Wang
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.
