有界噪声和谐和激励联合作用下一类非线性系统的混沌研究

研究一类有界噪声和谐和激励联合作用下的非线性系统，首先用多尺度方法将该系统约化，针对约化后的平均系统，利用随机Melnikov过程方法结合均方值准则导出随机系统可能产生混沌运动的临界条件，结果表明在一定的参数范围内，随着Weiner过程强度参数值的增大，混沌的临界激励幅值先递减继而递增. 同时，用两类数值方法即最大Lyapunov指数法和Poincare截面法验证了解析结果. 关键词：有界噪声多尺度随机Melnikov过程混沌

Homoclinic chaos in averaged oscillator subjected to combined deterministic and narrow-band random excitations

In the present paper, homoclinic chaos in averaged oscillator subjected to combined deterministic and narrow-band random excitations is investigated in detail. The method of multiple-scale is first used to reduce the oscillator subjected to combined deterministic and narrow-band random excitations to an averaged oscillator only under narrow-band random excitation. In order to determine the threshold of random excitation amplitude for the onset of chaos, the stochastic Melnikov technique is then applied to the averaged oscillator with mean-square criterion and it is found that the threshold of random excitation amplitude for the onset of chaos in the oscillator turns from increasing to decreasing as the intensity of the noise increases. On the other hand, another threshold of random excitation amplitude for the onset of chaos is obtained by calculating the largest Lyapunov exponents numerically. The Poincare maps are also used for verifying the conclusion. Qualitatively consistent results are obtained by the analytical and numerical methods.