参量激励作用下非线性系统的二参数分叉

Resonance Bifurcation of a Nonlinear System Under Parametrical Excitation

参量激励下的Duffing-van der Pol系统是一个多参数的非线性系统，本文研究了该系统的二参数共振分叉问题，利用多尺度方法得到了系统的一次近似平均方程和分叉响应方程，分析了分叉方程的解及其在二分叉参数平面上的分布，研究了零解的稳定性。

Duffing van der pol system is a nonlinear system .The two-parametrical resonance bifurcation of the system under parametrical excitation is explored.The average equation and bifurcation equation are derived with MSM.The solutions of the bifurcation equation, their distribution on the bifurcation parametrical plane and the stability of the zero solution are discussed respectively.