一类扰动的三次Z_2-等变向量场的极限环分支

Bifurcations of Limit Cycles in a Z_2-Equivariant Perturbed Cubic Vector Field

考虑一类扰动的平面三次Z2-等变Hamilton向量场,借助数值分析工具,利用平面动力系统分支理论和判定函数方法证明该向量场至少存在11个极限环,且给出这些极限环的相对位置分布.这对于研究弱化的Hilbert第16问题以及认识三次向量场的分支性质都具有非常重要的意义.

A class of perturbed cubic Z2 - equivariant Hamilton vector field is discussed in this paper. By using the bifurcation theory of planar dynamical systems and the method of detection functions, it is proved that there are at least 11 limit cycles in the system, which is significant to the study of weakening Hilbert＇s 16th problem and to the acquaintance of the characteristics of cubic vector field.