一类(Ⅱ)类二次系统的同宿轨分支极限环

The Problems of Homoclinic Bifurcation Limit Circle for Type(Ⅱ) Planar Quadratic Polynomial Systems

研究了一类特殊的二次系统(Ⅱ)类方程=-y+δx+mxy+ny2,=x(1+ax)的同宿轨分支极限环的存在性问题.运用分支方法,通过分析未扰系统的同宿轨经扰动破裂以后稳定流形和不稳定流形之间的相对距离,给出至少存在一个或两个极限环的条件.

By analyzing the homoclinic bifurcation after the homoclinic orbit of the unperturbed system was perturbed to break,the existence problems of limit cycles for the type （I）planar quadratic polynomial system was studied.A general condition was given to ensure the perturbed system has at least one or two limit cycle.