一类扰动的超椭圆Hamilton系统的极限环分布情况  

Limit Cycle Distribution of a Class of Perturbed Hyperelliptic Hamilton Systems

作　　者：王彦杰 洪晓春[1] WANG Yanjie;HONG Xiaochun(Institute of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650000,China)

机构地区：[1]云南财经大学统计与数学学院

出　　处：《湖北民族学院学报（自然科学版）》2019年第2期156-160,共5页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(11761075)

摘　　要：在定性分析理论指导下,运用判定函数和数值探测方法,研究了一类具有幂零鞍点的超椭圆Hamilton系统在多项式扰动下的极限环个数和分布问题,这里的多项式扰动共有3个任意参数.证明了该系统在无界周期环域中最多分出3个极限环,并运用数值模拟得到了3个极限环的准确位置.该研究成果有助于进一步研究希尔伯特的第16个问题.Under the guidance of qualitative analysis theory,using the detection function and numerical exploration method,we study the limit cycles number and distribution problem of a class of hyper-elliptic Hamiltonian systems with power zero saddle points under polynomial perturbation.Here,the polynomial perturbation has three arbitrary parameters.This paper proves that the system can divide up to three limit cycles in the unbounded periodic ring domain,and the exact position of the three limit cycles by numerical simulation is obtained.The research results can further study Hilbert′s 16th problem.

关 键 词：定性分析 判定函数 数值探测 超椭圆Hamilton系统 极限环 

分 类 号：O175.12[理学—数学]