【摘要】 本文用Melnikov函数方法讨论了一类扩张了的软弹簧型Duffing方程（?）+Af（（?）,x）+x-x^2k+1=r[M（x,（?））cosωt+N（x,（?））sinωt]（k=1,2,3,…）在周期激励下的紊动现象.给出了出现二阶同宿切的条件.文中所采用的方法对于不能给出并宿轨道的显式的系统的研究是非常有用的.更多还原

【Abstract】 In this paper, we use the Melnikov function method to study a kind of soft Duffing equations[1]and give the condition that the equations have chaotic motion and bifurcation. The method used in this paper is effective for dealing with the Melnikov function integral of the system whose explicit expression of the homoclinic or heteroclinic orbit cannot be given.更多还原