This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging method. The first algorithm allows one to transform the considered differential systems to the normal form of averaging. Here, we restricted the unperturbed term of the normal form of averaging to be identically zero. The second algorithm is used to derive the computational formulae of the averaged functions at any order. The third algorithm is based on the first two algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The proposed approach is implemented in Maple and its effectiveness is shown by several examples. Moreover, we report some incorrect results in published papers on the averaging method.

本文介绍了一种通过平均法分析非线性连续微分系统中心极限环分叉的算法。我们开发了三种算法来实现平均方法。第一种算法允许将考虑的差分系统转换为平均形式。在此，我们将平均平均形式的无扰项限制为相同的零。第二种算法用于以任何顺序导出平均函数的计算公式。第三种算法基于前两种算法，并确定了所考虑的微分系统的平均函数的精确表达式。所提出的方法在Maple中实现，其有效性通过几个示例说明。此外，