中文摘要：

研究了催化反应Flickering振子在多频率确定性谐和外力和有界随机噪声联合作用下,系统安全盆的侵蚀和混沌现象.将Melnikov方法推广到包含有限多个频率外力和随机噪声联合作用的情形,推导出了系统的随机Melnikov过程,根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值,然后用数值模拟方法计算了系统的安全盆分岔点.结果表明,由于随机扰动的影响,系统的安全盆分岔点发生了偏移,并且使得混沌容易发生.同时证明,激励频率数目的增加扩大了参数空间上的混沌区域,也使得安全盆分岔提前发生,系统变得不安全.

英文摘要：

The erosion of the safe basins and related chaotic motions of a Flickering oscillator under multi-frequency external periodic forces and bounded random noise are studied. By the Melnikov method, the system＇ s Melnikov integral is computed and the parametric threshold for the onset of chaos is obtained. The Melnikov＇ s global perturbation technique is therefore generalized to higher dimensional systems. Using the Monte-Carlo and Runge-Kutta method, the erosion of safe basins is also discussed. As an alternative definition, stochastic bifurcation may be defined as a sudden change in the character of stochastic safe basins when the bifurcation parameter of the system passes through a critical value. This definition applies equally well either to randomly perturbed motions or to purely deterministic motions. It is found that increasing the number of forcing frequencies or increasing the random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation and make the threshold for onset of chaos vary in a larger extent, which hence makes the system less safe and chaotic motions easier to occur.