一类近-Hamilton多项式系统的极限环分支问题  

Bifurcations of Limit Cycles in a Class of Near-Hamiltonian Polynomial Systems

作　　者：顾枸 熊艳琴 Gu Xun;Xiong Yanqin(School of Mathematics and Statistics,Nanjing university of information science&technology,Nanjing210044)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《数学物理学报(A辑)》2025年第2期604-618,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(12371171);江苏省自然科学基金面上项目(BK20221339)。

摘　　要：该文主要借助Abel积分来研究一类近-Hamilton多项式系统的极限环分支问题.首先,借助分析的技巧分别推出Abel积分在中心奇点处及异宿环附近的近似展开式并给出系数的计算表达式;这些结果可以用来研究扰动系统的Hopf分支及异宿分支问题.具体而言,所讨论的近-Hamilton多项式系统在中心奇点附近可产生[n+1/4]+[n-1/4]+1个极限环及在异宿环附近可分支出2[n+1/4]+[n-1/4]+1个极限环.This article primarily focuses on the study of the limit cycle bifurcation problem of a class of near-Hamiltonian polynomial systems using Abel integral.First,by utilizing analytical techniques,approximate expansions of Abel integral are derived around the central singularity and in the vicinity of the heteroclinic loop,along with the calculated expressions for the coeficients.These results can be utilized to analyze the Hopf bifurcation or heteroclinic bifurcation of the perturbed system.Specifically,it is shown that the discussed near-Hamiltonian polynomial system can produce [n+1/4]+[n-1/4]+1 limit cycles near the central singularity and branch out 2[n+1/4]+[n-1/4]+1 limit cycles near the heteroclinic loop.

关 键 词：近-Hamilton系统 极限环 ABEL积分 异宿分支 

分 类 号：O175.1[理学—数学]