摘要
研究一个7次Z_7-等变平面多项式干扰系统.利用平面动力系统的分支方法和判定函数方法,通过选择恰当的扰动系统参数以获得尽可能多的极限环个数.借助于数值计算,获得了35个极限环,并给出了这些极限环的复眼分布模式.
In this article,a general Z7-equivariant planar polynomial Hamiltonian system is considered.With the help of numerial analysis,bifurcation theory of planar dynamical systems and the method of detection function,the article intents to find more closed orbits and more limit cycles after perturbing the system.Following the special consideration of Z7-equivariant vector fields of degree7,35limit cycles are obtained and the configuration of compound eyes of that Z7-equivariant system are showed.
作者
周蒙蒙
石剑平
ZHOU Mengmeng;SHI Jianping(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China;Center For Nonlinear Science Studies,Kunming University of Science and Technology,Kunming 650500,China)
出处
《河南科学》
2017年第4期501-508,共8页
Henan Science
基金
国家自然科学基金项目(11561034)
云南省教育厅科学研究基金项目(2017zzx133)
关键词
极限环分支
Z7-等变平面干扰向量场
判定函数
异宿环和同宿环
扰动哈密顿系统
bifurcations of limit cycles
Z7-equivariant planar vector field
detection function
heteroclinic and homoclinic loops
perturbed Hamiltonian system
