超临界情形的Melnikov函数及应用

该文具体推导了三阶Melnikov函数的积分表达，解决了电机工程中提出的一类系统（见5]），当参数时的超临界（一阶、二阶Melnikov函数恒为零）的情形下，系统的稳定流形与不稳定流形的相对位置的确定问题．并通过环面上的VanderPol方程，对2]与4]所给的二阶Melnikov函数的表达式进行了比较，结果发现2]所给的平面自治系统的二阶，n阶表达式均是错的.该文在最后作了纠正.

Melnikov Function and Application in Supercritical Cases

This paper deduces the formula of the third order Melnikov function. the relativc positions of the stable manifold and unstable manifold of the systems in electrical engineeringare determined in supercritical cases, We make a comparison between the formulae of thesecond order Melnikov functions in 2]and 4]from studying of tora1 van der Pol equations )and find that the second order and the nth order formulae in 2]are wrong. Finaly,we correct this mistake.