有界噪声参激下Duffing振子混沌运动的解析方法

ANALYTIC METHODS FOR THE CHAOTIC MOTION OF DUFFING OSCILLATOR UNDER PARAMETRIC EXCITATION OF BOUNDED NOISE

研究有界噪声参激下Duffing振子出现混沌运动的可能性。推导了随机Melnikov过程 ,由广义过程在均方意义上出现简单零点给出了可能出现混沌的临界激励幅值 ,发现在噪声强度大于一定值后 。

The possibility for onset of chaotic motion in the Duffing oscillator under parametric excitation of bounded noise is studied. The stochastic Melnikov process is derived and the critical value of excitation amplitude for the onset of chaotic motion is obtained based on the stochastic Melnikov process having simple zero in the mean square sense. It is found that the critical values increase as the intensity of noise increases for larger value of noise intensity.