一类三维系统高阶奇点退化Hopf分岔的环性OA
Cyclicity of High-order Singular Point Degenerate Hopf Bifurcation for a Class of Three-dimensional Systems
本文研究一类三维系统在高阶奇点处发生的退化Hopf分岔.基于中心流形定理,给出一种直接计算奇点量的形式级数方法,避免将原三维系统转化为平面约化方程的繁琐过程,该算法对应的线性递推公式易于执行.具体研究一类四次系统,解决其高阶奇点的中心与退化Hopf分岔环性问题.
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.
姚洁;王勤龙
桂林电子科技大学 数学与计算科学学院,广西 桂林 541004桂林电子科技大学 数学与计算科学学院,广西 桂林 541004
数理科学
高阶奇点退化Hopf环性中心问题奇点量
higher-order singularitydegenerate Hopf cyclicitycenter problemsingular point quantities
《广西师范大学学报（自然科学版）》 2026 (1)
102-109,8
国家自然科学基金(12161023)广西自然科学基金(2025GXNSFAA069254)广西应用数学中心(广西师范大学)开放基金(CAMG2022A01)桂林电子科技大学研究生创新基金(2025YCXS125)
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