Holmes型Duffing方程的同宿轨道分支出的极限环

LIMITED CIRCLES BIFURCATED FROM HOMOCLINIC ORIBITS OF HOLMES' DUFFING EQUATIONS

用Melnikov函数方法对Holmes型Duffing方程d^2x/dt^1+δ(x^2+ax+c)dx/dt-ax+βx^3=0和更一般的形式d^2x/dt^2+δf(x)dx/dt-ax+βx^3=0进行了分析,得到了由同宿轨道分支出稳定不稳定极限环的条件.

In this paper,the author analysed Holmes' Duffing Equationd2x/dt2+δ(x2 + ax + c)dx/dt- ax +βx3 = 0and Its general form d2x/dt2+δf(x) dx/dt- ax +βx3 = 0 with Melikov Function method ,giving the conditims which stable on unstable limited circles are bifurcated from the homoclinic Oribits