摘要
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.
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.
出处
《数学物理学报(A辑)》
CSCD
北大核心
1997年第2期152-162,共11页
Acta Mathematica Scientia
关键词
双曲鞍点
稳定
流形
不稳定
同宿轨
混沌
<Keywards> hyperbolic saddle point , stable manifold, unstable manifold , homoclinic orbits ,heleroclinic orbits