广西师范大学学报（自然科学版）2026，Vol.44Issue(1)：102-109,8.DOI:10.16088/j.issn.1001-6600.2025012401
一类三维系统高阶奇点退化Hopf分岔的环性
Cyclicity of High-order Singular Point Degenerate Hopf Bifurcation for a Class of Three-dimensional Systems
摘要
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.关键词
高阶奇点/退化Hopf环性/中心问题/奇点量Key words
higher-order singularity/degenerate Hopf cyclicity/center problem/singular point quantities分类
数理科学引用本文复制引用
姚洁,王勤龙..一类三维系统高阶奇点退化Hopf分岔的环性[J].广西师范大学学报（自然科学版）,2026,44(1):102-109,8.基金项目
国家自然科学基金(12161023) （12161023）
广西自然科学基金(2025GXNSFAA069254) （2025GXNSFAA069254）
广西应用数学中心(广西师范大学)开放基金(CAMG2022A01) （广西师范大学）
桂林电子科技大学研究生创新基金(2025YCXS125) （2025YCXS125）
