【摘要】 对于非退化的多项式系统在小扰动下的分歧现象，只需计算一阶Ｍｅｌｎｉｋｏｖ函数及其孤立零点的个数．但是对于退化的复杂情况，则必须分析高阶Ｍｅｌｎｉｋｏｖ函数．此文利用轨道的渐近展开式和向量场的微分形式，给出了计算高阶Ｍｅｌｎｉｋｏｖ函数的两种方法更多还原

【Abstract】 For the bifurcation phenomenon of polynomial system under small perturbation, we only need to calculate the first order Melnikov function and zero points of it. But for the case of degenerate, we must analyse the higher order Melnikov function. In this paper, we provide two methods of calculation of higher order Melnikov function by expansion of orbit near the period solution and differential form of vector field.更多还原