有界噪声参激下Duffing振子混沌运动的数值方法

Numerical methods for the chaotic motion of duffing oscillator uuder parametric excitation of bounded noise

研究了有界噪声参激下Duffing振子出现混沌运动的可能性.用数值方法计算了该系统的最大Lyapunov指数,由最大Lyapunov指数为零,给出了出现混沌的临界激励幅值,发现在噪声强度大于一定值后,临界幅值均随噪声强度的增大而增大.

<Abstrcat>The possibility for onset of chaotic motion in the Duffing oscillator under parametric excitation of bounded noise is studied. The stochastic Melnikov process is first 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. Then, the largest Lyapunov exponent of the system is calculated numerically and the critical value of excitation amplitude is obtained based on vanishing of the largest Lyapunov exponent. It is found that both two critical values increase as the intensity of noise increases for larger value of noise intensity.